Table Of Content

Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: 10-1 Sequences as Functions Yes Determine whether each sequence is arithmetic 3. 1, 2, 4, 8, 16 no. SOLUTION: 1. 8, –2, –12, –22 Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: No ANSWER: Yes 4. 0.6, 0.9, 1.2, 1.8, ... 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: No ANSWER: Yes Find the next four terms of each arithmetic sequence. Then graph the sequence. 3. 1, 2, 4, 8, 16 5. 6, 18, 30, … SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. There is no common difference. The common difference is 12. Therefore, the sequence is not arithmetic. Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. ANSWER: 30 + 12 = 42 No eSolutionsManual-PoweredbyCognero 42 + 12 = 54 Page1 54 + 12 = 66 66 + 12 = 78 4. 0.6, 0.9, 1.2, 1.8, ... Graph the sequence. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No ANSWER: 42, 54, 66, 78 Find the next four terms of each arithmetic sequence. Then graph the sequence. 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. 6. 15, 6, –3, … The common difference is 12. Therefore, the sequence is arithmetic. SOLUTION: To find the next term, add 12 to the last term. Subtract each term from the term directly after it. 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 66 + 12 = 78 Graph the sequence. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add –9 to the last term. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 Graph the sequence. ANSWER: 42, 54, 66, 78 ANSWER: –12, –21, –30, –39 6. 15, 6, –3, … SOLUTION: Subtract each term from the term directly after it. 7. –19, –11, –3, … The common difference is –9. SOLUTION: Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the next term, add –9 to the last term. –3 + (–9) = –12 –12 + (–9) = –21 The common difference is 8. –21 + (–9) = –30 Therefore, the sequence is arithmetic. –30 + (–9) = –39 To find the next term, add 8 to the last term. Graph the sequence. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. ANSWER: –12, –21, –30, –39 ANSWER: 5, 13, 21, 29 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. 8. –26, –33, –40, … The common difference is 8. Therefore, the sequence is arithmetic. SOLUTION: Subtract each term from the term directly after it. To find the next term, add 8 to the last term. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 The common difference is –7. 21 + 8 = 29 Therefore, the sequence is arithmetic. Graph the sequence. To find the next term, add –7 to the last term. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 –61 + (–7) = –68 Graph the sequence. ANSWER: 5, 13, 21, 29 ANSWER: –47, –54, –61, –68 8. –26, –33, –40, … SOLUTION: Subtract each term from the term directly after it. 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to The common difference is –7. save $75 per week from her job as a waitress. Therefore, the sequence is arithmetic. a. How much will Kelly have saved after 8 weeks? To find the next term, add –7 to the last term. b. If the car costs $2000, how long will it take her to –40 + (–7) = –47 save enough money at this rate? –47 + (–7) = –54 –54 + (–7) = –61 –61 + (–7) = –68 SOLUTION: a. Given a = 250, d = 75 and n = 8. Graph the sequence. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. b. Given a = 2000. n Find n. ANSWER: So, it will take about 24 weeks to save $2000. –47, –54, –61, –68 ANSWER: a. $850 b. 24 wk Determine whether each sequence is geometric. Write yes or no. 10. –8, –5, –1, 4, … 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. SOLUTION: Find the ratio of the consecutive terms. a. How much will Kelly have saved after 8 weeks? b. If the car costs $2000, how long will it take her to save enough money at this rate? Since the ratios are not same, the sequence is not geometric. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 ANSWER: After 8 weeks, she will have 250 + (8 × 75) or $850. No b. Given a = 2000. n Find n. 11. 4, 12, 36, 108, … SOLUTION: Find the ratio of the consecutive terms. So, it will take about 24 weeks to save $2000. Since the ratios are the same, the sequence is ANSWER: geometric. a. $850 ANSWER: b. 24 wk Yes Determine whether each sequence is 12. 27, 9, 3, 1, … geometric. Write yes or no. 10. –8, –5, –1, 4, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are not same, the sequence is not geometric. ANSWER: Yes ANSWER: No 13. 7, 14, 21, 28, … SOLUTION: 11. 4, 12, 36, 108, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Since the ratios are the same, the sequence is geometric. ANSWER: No ANSWER: Yes Find the next three terms of each geometric sequence. Then graph the sequence. 12. 27, 9, 3, 1, … 14. 8, 12, 18, 27, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is Since the ratios are the same, the sequence is geometric. geometric To find the next term, multiply the previous term by ANSWER: Yes . 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not the same, the sequence is not geometric. ANSWER: No Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … ANSWER: 40.5, 60.75, 91.125 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 2. Graph the sequence. ANSWER: 40.5, 60.75, 91.125 ANSWER: 128, 256, 512 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. 16. 250, 50, 10, 2, … To find the next term, multiply the previous term by 2. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is Graph the sequence. geometric To find the next term, multiply the previous term by . ANSWER: 128, 256, 512 Graph the sequence. 16. 250, 50, 10, 2, … ANSWER: SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 17. 9, –3, 1, , … ANSWER: SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 18. 5, 1, 7, 3, 9, … SOLUTION: Graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. ANSWER: ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. Determine whether each sequence is arithmetic, geometric, or neither. Explain your There is no common difference. reasoning. Therefore, the sequence is not arithmetic. 18. 5, 1, 7, 3, 9, … Find the ratio of the consecutive terms. SOLUTION: The common ratio is . There is no common difference. Therefore, the sequence is not arithmetic. Since the ratios are the same, the sequence is geometric. Find the ratio of the consecutive terms. ANSWER: Geometric; the common ratio is . Since the ratios are not the same, the sequence is not geometric. 20. 12, 16, 20, 24, … ANSWER: Neither; there is no common difference or ratio. SOLUTION: To find the common difference, subtract any term from the term directly after it. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term The common difference is 4. from the term directly after it. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. Since the ratios are not the same, the sequence is not Find the ratio of the consecutive terms. geometric. ANSWER: Arithmetic; the common difference is 4. The common ratio is . Determine whether each sequence is arithmetic. Write yes or no. Since the ratios are the same, the sequence is geometric. 21. ANSWER: Geometric; the common ratio is . SOLUTION: Subtract any term from the term directly after it. 20. 12, 16, 20, 24, … SOLUTION: To find the common difference, subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: The common difference is 4. No Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. 22. –9, –3, 0, 3, 9 SOLUTION: Subtract any term from the term directly after it. Since the ratios are not the same, the sequence is not geometric. ANSWER: There is no common difference. Arithmetic; the common difference is 4. Therefore, the sequence is not arithmetic. Determine whether each sequence is ANSWER: arithmetic. Write yes or no. No 21. 23. 14, –5, –19, … SOLUTION: SOLUTION: Subtract any term from the term directly after it. Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No ANSWER: No 24. 22. –9, –3, 0, 3, 9 SOLUTION: SOLUTION: Subtract any term from the term directly after it. Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. The common difference is . Therefore, the sequence is arithmetic. ANSWER: No ANSWER: Yes 23. 14, –5, –19, … Find the next four terms of each arithmetic SOLUTION: sequence. Then graph the sequence. Subtract any term from the term directly after it. 25. –4, –1, 2, 5,… SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No The common difference is 3. Therefore, the sequence is arithmetic. To find the next term, add 3 to the last term. 24. 5 + 3 = 8 8 + 3 = 11 SOLUTION: 11 + 3 = 14 Subtract any term from the term directly after it. 14 + 3 = 17 Graph the sequence. The common difference is . Therefore, the sequence is arithmetic. ANSWER: Yes ANSWER: Find the next four terms of each arithmetic 8, 11, 14, 17 sequence. Then graph the sequence. 25. –4, –1, 2, 5,… SOLUTION: Subtract any term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. 26. 10, 2, –6, –14, … To find the next term, add 3 to the last term. SOLUTION: Subtract any term from the term directly after it. 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 14 + 3 = 17 Graph the sequence. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. –14 + (–8) = –22 –22 + (–8) = –30 –30 + (–8) = –38 –38 + (–8) = –46 Graph the sequence. ANSWER: 8, 11, 14, 17 ANSWER: –22, –30, –38, – 46 26. 10, 2, –6, –14, … SOLUTION: Subtract any term from the term directly after it. The common difference is –8. 27. –5, –11, –17, –23, … Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. SOLUTION: Subtract any term from the term directly after it. –14 + (–8) = –22 –22 + (–8) = –30 –30 + (–8) = –38 –38 + (–8) = –46 Graph the sequence. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. –23 + (–6) = –29 –29 + (–6) = –35 –35 + (–6) = –41 –41 + (–6) = –47 Graph the sequence. ANSWER: –22, –30, –38, – 46 ANSWER: –29, –35, – 41, – 47 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. 28. –19, –2, 15, … To find the next term, add –6 to the last term. –23 + (–6) = –29 SOLUTION: –29 + (–6) = –35 Subtract any term from the term directly after it. –35 + (–6) = –41 –41 + (–6) = –47 Graph the sequence. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 Graph the sequence. ANSWER: –29, –35, – 41, – 47 ANSWER: 32, 49, 66, 83 28. –19, –2, 15, … SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. 29. To find the next term, add 17 to the last term. SOLUTION: 15 + 17 = 32 Subtract any term from the term directly after it. 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 Graph the sequence. The common difference is . Therefore, the sequence is arithmetic. To find the next term, add to the last term. ANSWER: 32, 49, 66, 83 Graph the sequence. 29. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is . Therefore, the sequence is arithmetic. To find the next term, add to the last term. 30. SOLUTION: Subtract any term from the term directly after it. Graph the sequence. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. ANSWER: Graph the sequence. 30. ANSWER: SOLUTION: Subtract any term from the term directly after it. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: Given a = 28, d = 2 and n = 24. 1 Graph the sequence. Find a . 24 ANSWER: 74 ANSWER: 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue indefinitely? Explain. SOLUTION: 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more a. Given a = 5, d = 1.5 and n = 18. 1 seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? Find a . 18 SOLUTION: Given a = 28, d = 2 and n = 24. 1 Find a24. Therefore he will row for 30 minutes and 30 seconds on the 38th day. b. Given a = 5, d = 1.5 and a = 60. 1 n Find n. ANSWER: 74 32. CCSS SENSE-MAKING Mario began an exercise Mario will first row an hour or more on the 38th day. program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and c. Sample answer: It is unreasonable because there increase his rowing time by one minute and thirty are only so many hours in the day that can be seconds each day. dedicated to rowing. a. How long will he row on the 18th day? ANSWER: a. 30 minutes and 30 seconds b. On what day will Mario first row an hour or more? b. on the 38th day c. Is it reasonable for this pattern to continue indefinitely? Explain. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing. SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Determine whether each sequence is geometric. Write yes or no. Find a . 18 33. 21, 14, 7, … SOLUTION: Therefore he will row for 30 minutes and 30 seconds Find the ratio of the consecutive terms. on the 38th day. b. Given a = 5, d = 1.5 and a = 60. 1 n Find n. Since the ratios are not the same, the sequence is not geometric. ANSWER: No Mario will first row an hour or more on the 38th day. c. Sample answer: It is unreasonable because there 34. 124, 186, 248, … are only so many hours in the day that can be dedicated to rowing. SOLUTION: Find the ratio of the consecutive terms. ANSWER: a. 30 minutes and 30 seconds b. on the 38th day Since the ratios are not the same, the sequence is not c. Sample answer: It is unreasonable because there geometric. are only so many hours in the day that can be dedicated to rowing. ANSWER: No Determine whether each sequence is geometric. Write yes or no. 35. –27, 18, –12, … 33. 21, 14, 7, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Since the ratios are the same, the sequence is Find the ratio of the consecutive terms. geometric. ANSWER: Yes Since the ratios are not the same, the sequence is not 36. 162, 108, 72, … geometric. SOLUTION: ANSWER: Find the ratio of the consecutive terms. No 34. 124, 186, 248, … Since the ratios are same, the sequence is geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: Yes 37. Since the ratios are not the same, the sequence is not geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: No 35. –27, 18, –12, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Since the ratios are not same, the sequence is not Yes geometric. 36. 162, 108, 72, … ANSWER: SOLUTION: No Find the ratio of the consecutive terms. 38. –4, –2, 0, 2, … SOLUTION: Since the ratios are same, the sequence is geometric. Find the ratio of the consecutive terms. ANSWER: Yes Since the ratios are not same, the sequence is not geometric. 37. ANSWER: No SOLUTION: Find the ratio of the consecutive terms. Find the next three terms of the sequence. Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric Since the ratios are not same, the sequence is not geometric. To find the next term, multiply the previous term with −4. ANSWER: No 38. –4, –2, 0, 2, … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: No ANSWER: Find the next three terms of the sequence. – 8, 32, –128 Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric 40. 18, 12, 8, … To find the next term, multiply the previous term with −4. SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: – 8, 32, –128 Graph the sequence. 40. 18, 12, 8, … ANSWER: SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . 41. 64, 48, 36, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: Graph the sequence. ANSWER: 41. 64, 48, 36, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . ANSWER: Graph the sequence. ANSWER: 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . 43. SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. Graph the sequence. ANSWER: ANSWER: 27, 81, 243 43. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 44. 1, 0.1, 0.01, 0.001, … 3. SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. Graph the sequence. ANSWER: 27, 81, 243 ANSWER: 0.0001, 0.00001, 0.000001 44. 1, 0.1, 0.01, 0.001, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Determine whether each sequence is 0.1. arithmetic, geometric, or neither. Explain your reasoning. 45. 3, 12, 27, 48, … SOLUTION: Graph the sequence. Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. ANSWER: 0.0001, 0.00001, 0.000001 Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … SOLUTION: Subtract each term from the term directly after it. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 45. 3, 12, 27, 48, … The common difference is –3. Therefore, the sequence is arithmetic. SOLUTION: Subtract each term from the term directly after it. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Since the ratios are not same, the sequence is not geometric. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the ANSWER: consecutive terms. Arithmetic; the common difference is –3. 47. 12, 36, 108, 324, … Since the ratios are not same, the sequence is not geometric. SOLUTION: Subtract each term from the term directly after it. ANSWER: Neither; there is no common difference or ratio. There is no common difference. 46. 1, –2, –5, –8, … Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the SOLUTION: consecutive terms. Subtract each term from the term directly after it. The common ratio is 3. The common difference is –3. Therefore, the sequence is arithmetic. Since the ratios are same, the sequence is geometric. To find the common ratio, find the ratio of the consecutive terms. ANSWER: Geometric; the common ratio is 3. Since the ratios are not same, the sequence is not 48. geometric. ANSWER: SOLUTION: Arithmetic; the common difference is –3. Subtract each term from the term directly after it. 47. 12, 36, 108, 324, … SOLUTION: There is no common difference. Subtract each term from the term directly after it. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common ratio is . Since the ratios are the same, the sequence is geometric. The common ratio is 3. Since the ratios are same, the sequence is geometric. ANSWER: Geometric; the common ratio is . ANSWER: Geometric; the common ratio is 3. 49. 48. SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is . There is no common difference. Therefore, the sequence is arithmetic. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the To find the common ratio, find the ratio of the consecutive terms. consecutive terms. Since the ratios are not same, the sequence is not The common ratio is . geometric. Since the ratios are the same, the sequence is ANSWER: geometric. Arithmetic; the common difference is . ANSWER: Geometric; the common ratio is . 50. 6, 9, 14, 21, … SOLUTION: Subtract each term from the term directly after it. 49. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common difference is . Therefore, the sequence is arithmetic. Since the ratios are not same, the sequence is not geometric. To find the common ratio, find the ratio of the consecutive terms. ANSWER: Neither; there is no common difference or ratio. 51. READING Sareeta took an 800-page book on Since the ratios are not same, the sequence is not vacation. If she was already on page 112 and is geometric. going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation? ANSWER: Arithmetic; the common difference is . SOLUTION: The number of pages to be read is 800 – 112 or 688. The minimum number of pages to read per day is 50. 6, 9, 14, 21, … . SOLUTION: Subtract each term from the term directly after it. ANSWER: 86 pg/day There is no common difference. 52. DEPRECIATION Tammy’s car is expected to Therefore, the sequence is not arithmetic. depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, To find the common ratio, find the ratio of the how much will it be worth in 6 years? consecutive terms. SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in then evaluate. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. The worth of the car will be about $9052 after 6 years. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is ANSWER: going to be on vacation for 8 days, what is the $9052 minimum number of pages she needs to read per day to finish the book by the end of her vacation? 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of SOLUTION: paper that is 0.1 mm thick could be folded 37 times, The number of pages to be read is 800 – 112 or 688. how thick would it be? The minimum number of pages to read per day is SOLUTION: . Given a = 0.1, n = 37 and r = 2. 0 Find a . 37 ANSWER: 86 pg/day 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, The thickness would be about 13,744 km. how much will it be worth in 6 years? ANSWER: SOLUTION: about 13,744 km Substitute 0.15, 6 and 24000 for r, t and P in then evaluate. 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. SOLUTION: The worth of the car will be about $9052 after 6 Sample answer: The consecutive terms do not share years. a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. ANSWER: ANSWER: $9052 Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, 53. CCSS REGULARITY When a piece of paper is while 17 – 13 = 4. folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, how thick would it be? 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. SOLUTION: Given a = 0.1, n = 37 and r = 2. 0 SOLUTION: Sample answer: A babysitter earns $20 for cleaning Find a . the house and $8 extra for every hour she watches 37 the children. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. The thickness would be about 13,744 km. 56. CHALLENGE The sum of three consecutive terms ANSWER: of an arithmetic sequence is 6. The product of the about 13,744 km terms is –42. Find the terms. SOLUTION: 54. REASONING Explain why the sequence 8, 10, 13, Let x be the first term in the arithmetic sequence. 17, 22 is not arithmetic. Therefore, the next two terms should be x + d and x + 2d. SOLUTION: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. ANSWER: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. Sample answer: 55. OPEN ENDED Describe a real-life situation that Let d = 5. can be represented by an arithmetic sequence with a Therefore, the terms are –3, 2, 7. common difference of 8. ANSWER: –3, 2, 7 SOLUTION: Sample answer: A babysitter earns $20 for cleaning 57. ERROR ANALYSIS Brody and Gen are the house and $8 extra for every hour she watches determining whether the sequence 8, 8, 8,… is the children. arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. Sample answer: Let d = 5. 58. OPEN ENDED Find a geometric sequence, an Therefore, the terms are –3, 2, 7. arithmetic sequence, and a sequence that is neither ANSWER: geometric nor arithmetic that begins 3, 9,… . –3, 2, 7 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Yes 3. 1, 2, 4, 8, 16 SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. Determine whether each sequence is arithmetic no. ANSWER: No 1. 8, –2, –12, –22 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. There is no common difference. ANSWER: Therefore, the sequence is not arithmetic. Yes ANSWER: 2. –19, –12, –5, 2, 9 No SOLUTION: Find the next four terms of each arithmetic Subtract each term from the term directly after it. sequence. Then graph the sequence. 5. 6, 18, 30, … SOLUTION: The common difference is 7. Subtract each term from the term directly after it. Therefore, the sequence is arithmetic. ANSWER: Yes The common difference is 12. Therefore, the sequence is arithmetic. 3. 1, 2, 4, 8, 16 To find the next term, add 12 to the last term. 30 + 12 = 42 SOLUTION: 42 + 12 = 54 Subtract each term from the term directly after it. 54 + 12 = 66 66 + 12 = 78 Graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: ANSWER: Subtract each term from the term directly after it. 42, 54, 66, 78 There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: 10-1N Soe quences as Functions Find the next four terms of each arithmetic 6. 15, 6, –3, … sequence. Then graph the sequence. SOLUTION: 5. 6, 18, 30, … Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is –9. Therefore, the sequence is arithmetic. The common difference is 12. To find the next term, add –9 to the last term. Therefore, the sequence is arithmetic. –3 + (–9) = –12 To find the next term, add 12 to the last term. –12 + (–9) = –21 30 + 12 = 42 –21 + (–9) = –30 42 + 12 = 54 –30 + (–9) = –39 54 + 12 = 66 66 + 12 = 78 Graph the sequence. Graph the sequence. ANSWER: –12, –21, –30, –39 ANSWER: 42, 54, 66, 78 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. 6. 15, 6, –3, … eSolutSioOnsLMUanTuIaOl-NPo: w eredbyCognero Page2 Subtract each term from the term directly after it. The common difference is 8. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. The common difference is –9. –3 + 8 = 5 Therefore, the sequence is arithmetic. 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 To find the next term, add –9 to the last term. Graph the sequence. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 Graph the sequence. ANSWER: 5, 13, 21, 29 ANSWER: –12, –21, –30, –39 8. –26, –33, –40, … SOLUTION: Subtract each term from the term directly after it. 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. The common difference is –7. Therefore, the sequence is arithmetic. To find the next term, add –7 to the last term. The common difference is 8. Therefore, the sequence is arithmetic. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 To find the next term, add 8 to the last term. –61 + (–7) = –68 –3 + 8 = 5 Graph the sequence. 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. ANSWER: –47, –54, –61, –68 ANSWER: 5, 13, 21, 29 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. 8. –26, –33, –40, … a. How much will Kelly have saved after 8 weeks? b. If the car costs $2000, how long will it take her to SOLUTION: save enough money at this rate? Subtract each term from the term directly after it. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. The common difference is –7. Therefore, the sequence is arithmetic. b. Given a = 2000. n To find the next term, add –7 to the last term. Find n. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 –61 + (–7) = –68 Graph the sequence. So, it will take about 24 weeks to save $2000. ANSWER: a. $850 b. 24 wk Determine whether each sequence is geometric. Write yes or no. ANSWER: 10. –8, –5, –1, 4, … –47, –54, –61, –68 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. 9. FINANCIAL LITERACY Kelly is saving her ANSWER: money to buy a car. She has $250, and she plans to No save $75 per week from her job as a waitress. a. How much will Kelly have saved after 8 weeks? 11. 4, 12, 36, 108, … b. If the car costs $2000, how long will it take her to save enough money at this rate? SOLUTION: Find the ratio of the consecutive terms. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. Since the ratios are the same, the sequence is b. Given an = 2000. geometric. Find n. ANSWER: Yes 12. 27, 9, 3, 1, … So, it will take about 24 weeks to save $2000. SOLUTION: Find the ratio of the consecutive terms. ANSWER: a. $850 b. 24 wk Since the ratios are the same, the sequence is geometric. Determine whether each sequence is geometric. Write yes or no. ANSWER: 10. –8, –5, –1, 4, … Yes SOLUTION: 13. 7, 14, 21, 28, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are not the same, the sequence is not ANSWER: geometric. No ANSWER: No 11. 4, 12, 36, 108, … Find the next three terms of each geometric SOLUTION: sequence. Then graph the sequence. Find the ratio of the consecutive terms. 14. 8, 12, 18, 27, … SOLUTION: Since the ratios are the same, the sequence is Find the ratio of the consecutive terms. geometric. ANSWER: Yes Since the ratios are the same, the sequence is geometric 12. 27, 9, 3, 1, … To find the next term, multiply the previous term by . SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Graph the sequence. ANSWER: Yes 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are not the same, the sequence is not geometric. 40.5, 60.75, 91.125 ANSWER: No Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … SOLUTION: Find the ratio of the consecutive terms. 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by Since the ratios are the same, the sequence is . geometric. To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 128, 256, 512 40.5, 60.75, 91.125 16. 250, 50, 10, 2, … 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. 17. 9, –3, 1, , … Since the ratios are the same, the sequence is geometric SOLUTION: Find the ratio of the consecutive terms. To find the next term, multiply the previous term by . Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 18. 5, 1, 7, 3, 9, … Since the ratios are the same, the sequence is geometric. SOLUTION: To find the next term, multiply the previous term by . There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not Graph the sequence. geometric. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. ANSWER: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. The common ratio is . Determine whether each sequence is Since the ratios are the same, the sequence is arithmetic, geometric, or neither. Explain your geometric. reasoning. 18. 5, 1, 7, 3, 9, … ANSWER: Geometric; the common ratio is . SOLUTION: 20. 12, 16, 20, 24, … There is no common difference. Therefore, the sequence is not arithmetic. SOLUTION: To find the common difference, subtract any term Find the ratio of the consecutive terms. from the term directly after it. Since the ratios are not the same, the sequence is not The common difference is 4. geometric. Therefore, the sequence is arithmetic. ANSWER: Find the ratio of the consecutive terms. Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … Since the ratios are not the same, the sequence is not geometric. SOLUTION: To find the common difference, subtract any term ANSWER: from the term directly after it. Arithmetic; the common difference is 4. Determine whether each sequence is arithmetic. Write yes or no. There is no common difference. Therefore, the sequence is not arithmetic. 21. Find the ratio of the consecutive terms. SOLUTION: Subtract any term from the term directly after it. The common ratio is . Since the ratios are the same, the sequence is geometric. There is no common difference. ANSWER: Therefore, the sequence is not arithmetic. Geometric; the common ratio is . ANSWER: No 20. 12, 16, 20, 24, … 22. –9, –3, 0, 3, 9 SOLUTION: To find the common difference, subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 4. Therefore, the sequence is arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. ANSWER: No Since the ratios are not the same, the sequence is not 23. 14, –5, –19, … geometric. SOLUTION: ANSWER: Subtract any term from the term directly after it. Arithmetic; the common difference is 4. Determine whether each sequence is arithmetic. Write yes or no. There is no common difference. Therefore, the sequence is not arithmetic. 21. ANSWER: SOLUTION: No Subtract any term from the term directly after it. 24. SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No The common difference is . 22. –9, –3, 0, 3, 9 Therefore, the sequence is arithmetic. SOLUTION: ANSWER: Subtract any term from the term directly after it. Yes Find the next four terms of each arithmetic sequence. Then graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. 25. –4, –1, 2, 5,… ANSWER: SOLUTION: No Subtract any term from the term directly after it. 23. 14, –5, –19, … SOLUTION: The common difference is 3. Subtract any term from the term directly after it. Therefore, the sequence is arithmetic. To find the next term, add 3 to the last term. 5 + 3 = 8 8 + 3 = 11 There is no common difference. 11 + 3 = 14 Therefore, the sequence is not arithmetic. 14 + 3 = 17 Graph the sequence. ANSWER: No 24. SOLUTION: Subtract any term from the term directly after it. ANSWER: 8, 11, 14, 17 The common difference is . Therefore, the sequence is arithmetic. ANSWER: Yes Find the next four terms of each arithmetic sequence. Then graph the sequence. 26. 10, 2, –6, –14, … 25. –4, –1, 2, 5,… SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. The common difference is 3. Therefore, the sequence is arithmetic. To find the next term, add –8 to the last term. To find the next term, add 3 to the last term. –14 + (–8) = –22 –22 + (–8) = –30 5 + 3 = 8 –30 + (–8) = –38 8 + 3 = 11 –38 + (–8) = –46 11 + 3 = 14 14 + 3 = 17 Graph the sequence. Graph the sequence. ANSWER: –22, –30, –38, – 46 ANSWER: 8, 11, 14, 17 27. –5, –11, –17, –23, … 26. 10, 2, –6, –14, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –6 to the last term. To find the next term, add –8 to the last term. –23 + (–6) = –29 –29 + (–6) = –35 –14 + (–8) = –22 –35 + (–6) = –41 –22 + (–8) = –30 –41 + (–6) = –47 –30 + (–8) = –38 –38 + (–8) = –46 Graph the sequence. Graph the sequence. ANSWER: ANSWER: –29, –35, – 41, – 47 –22, –30, –38, – 46 27. –5, –11, –17, –23, … 28. –19, –2, 15, … SOLUTION: SOLUTION: Subtract any term from the term directly after it. Subtract any term from the term directly after it. The common difference is –6. The common difference is 17. Therefore, the sequence is arithmetic. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. To find the next term, add 17 to the last term. –23 + (–6) = –29 15 + 17 = 32 –29 + (–6) = –35 32 + 17 = 49 –35 + (–6) = –41 49 + 17 = 66 –41 + (–6) = –47 66 + 17 = 83 Graph the sequence. Graph the sequence. ANSWER: ANSWER: 32, 49, 66, 83 –29, –35, – 41, – 47 29. 28. –19, –2, 15, … SOLUTION: SOLUTION: Subtract any term from the term directly after it. Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. The common difference is . To find the next term, add 17 to the last term. Therefore, the sequence is arithmetic. 15 + 17 = 32 32 + 17 = 49 To find the next term, add to the last term. 49 + 17 = 66 66 + 17 = 83 Graph the sequence. Graph the sequence. ANSWER: 32, 49, 66, 83 ANSWER: 29. SOLUTION: Subtract any term from the term directly after it. 30. The common difference is . SOLUTION: Therefore, the sequence is arithmetic. Subtract any term from the term directly after it. To find the next term, add to the last term. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 30. SOLUTION: Subtract any term from the term directly after it. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? The common difference is –1. Therefore, the sequence is arithmetic. SOLUTION: Given a = 28, d = 2 and n = 24. 1 To find the next term, add −1 to the last term. Find a . 24 ANSWER: 74 Graph the sequence. 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or more? ANSWER: c. Is it reasonable for this pattern to continue indefinitely? Explain. SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Find a . 18 Therefore he will row for 30 minutes and 30 seconds on the 38th day. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more b. Given a = 5, d = 1.5 and a = 60. 1 n seats than the previous row. If there are 24 rows, Find n. how many seats are in the last row of the theater? SOLUTION: Given a = 28, d = 2 and n = 24. 1 Find a . Mario will first row an hour or more on the 38th day. 24 c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing. ANSWER: ANSWER: a. 30 minutes and 30 seconds 74 b. on the 38th day 32. CCSS SENSE-MAKING Mario began an exercise c. Sample answer: It is unreasonable because there program to get back in shape. He plans to row 5 are only so many hours in the day that can be minutes on his rowing machine the first day and dedicated to rowing. increase his rowing time by one minute and thirty seconds each day. Determine whether each sequence is a. How long will he row on the 18th day? geometric. Write yes or no. b. On what day will Mario first row an hour or 33. 21, 14, 7, … more? c. Is it reasonable for this pattern to continue SOLUTION: indefinitely? Explain. Find the ratio of the consecutive terms. SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Find a . Since the ratios are not the same, the sequence is not 18 geometric. ANSWER: No Therefore he will row for 30 minutes and 30 seconds on the 38th day. 34. 124, 186, 248, … b. Given a = 5, d = 1.5 and a = 60. 1 n Find n. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not Mario will first row an hour or more on the 38th day. geometric. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be ANSWER: dedicated to rowing. No ANSWER: 35. –27, 18, –12, … a. 30 minutes and 30 seconds SOLUTION: Find the ratio of the consecutive terms. b. on the 38th day c. Sample answer: It is unreasonable because there Since the ratios are the same, the sequence is are only so many hours in the day that can be geometric. dedicated to rowing. ANSWER: Yes Determine whether each sequence is geometric. Write yes or no. 36. 162, 108, 72, … 33. 21, 14, 7, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. Since the ratios are not the same, the sequence is not ANSWER: geometric. Yes ANSWER: No 37. SOLUTION: 34. 124, 186, 248, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. ANSWER: No Since the ratios are not same, the sequence is not geometric. 35. –27, 18, –12, … ANSWER: SOLUTION: No Find the ratio of the consecutive terms. 38. –4, –2, 0, 2, … Since the ratios are the same, the sequence is geometric. SOLUTION: ANSWER: Find the ratio of the consecutive terms. Yes 36. 162, 108, 72, … Since the ratios are not same, the sequence is not SOLUTION: geometric. Find the ratio of the consecutive terms. ANSWER: No Since the ratios are same, the sequence is geometric. Find the next three terms of the sequence. Then graph the sequence. ANSWER: Yes 39. 0.125, –0.5, 2, … SOLUTION: 37. Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: No 38. –4, –2, 0, 2, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: – 8, 32, –128 Since the ratios are not same, the sequence is not geometric. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. 40. 18, 12, 8, … 39. 0.125, –0.5, 2, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by To find the next term, multiply the previous term with . −4. Graph the sequence. Graph the sequence. ANSWER: – 8, 32, –128 ANSWER: 40. 18, 12, 8, … SOLUTION: Find the ratio of the consecutive terms. 41. 64, 48, 36, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 41. 64, 48, 36, … SOLUTION: 42. 81, 108, 144, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric . To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. 43. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 27, 81, 243 43. 44. 1, 0.1, 0.01, 0.001, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by To find the next term, multiply the previous term by 0.1. 3. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 0.0001, 0.00001, 0.000001 27, 81, 243 Determine whether each sequence is 44. 1, 0.1, 0.01, 0.001, … arithmetic, geometric, or neither. Explain your reasoning. SOLUTION: 45. 3, 12, 27, 48, … Find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … ANSWER: 0.0001, 0.00001, 0.000001 SOLUTION: Subtract each term from the term directly after it. The common difference is –3. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. Since the ratios are not same, the sequence is not geometric. 45. 3, 12, 27, 48, … ANSWER: SOLUTION: Arithmetic; the common difference is –3. Subtract each term from the term directly after it. 47. 12, 36, 108, 324, … SOLUTION: There is no common difference. Subtract each term from the term directly after it. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. The common ratio is 3. Since the ratios are same, the sequence is geometric. 46. 1, –2, –5, –8, … ANSWER: SOLUTION: Geometric; the common ratio is 3. Subtract each term from the term directly after it. 48. The common difference is –3. Therefore, the sequence is arithmetic. SOLUTION: Subtract each term from the term directly after it. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Since the ratios are not same, the sequence is not Therefore, this sequence is not arithmetic. geometric. To find the common ratio, find the ratio of the consecutive terms. ANSWER: Arithmetic; the common difference is –3. 47. 12, 36, 108, 324, … The common ratio is . SOLUTION: Subtract each term from the term directly after it. Since the ratios are the same, the sequence is geometric. ANSWER: There is no common difference. Therefore, this sequence is not arithmetic. Geometric; the common ratio is . To find the common ratio, find the ratio of the consecutive terms. 49. SOLUTION: The common ratio is 3. Subtract each term from the term directly after it. Since the ratios are same, the sequence is geometric. ANSWER: Geometric; the common ratio is 3. The common difference is . Therefore, the sequence is arithmetic. 48. To find the common ratio, find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not geometric. There is no common difference. Therefore, this sequence is not arithmetic. ANSWER: To find the common ratio, find the ratio of the Arithmetic; the common difference is . consecutive terms. 50. 6, 9, 14, 21, … SOLUTION: The common ratio is . Subtract each term from the term directly after it. Since the ratios are the same, the sequence is geometric. There is no common difference. ANSWER: Therefore, the sequence is not arithmetic. Geometric; the common ratio is . To find the common ratio, find the ratio of the consecutive terms. 49. Since the ratios are not same, the sequence is not SOLUTION: geometric. Subtract each term from the term directly after it. ANSWER: Neither; there is no common difference or ratio. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is The common difference is . going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day Therefore, the sequence is arithmetic. to finish the book by the end of her vacation? To find the common ratio, find the ratio of the consecutive terms. SOLUTION: The number of pages to be read is 800 – 112 or 688. The minimum number of pages to read per day is . Since the ratios are not same, the sequence is not geometric. ANSWER: ANSWER: 86 pg/day Arithmetic; the common difference is . 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is 50. 6, 9, 14, 21, … currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? SOLUTION: Subtract each term from the term directly after it. SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in then evaluate. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the The worth of the car will be about $9052 after 6 consecutive terms. years. ANSWER: $9052 Since the ratios are not same, the sequence is not geometric. 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, ANSWER: how thick would it be? Neither; there is no common difference or ratio. SOLUTION: 51. READING Sareeta took an 800-page book on Given a = 0.1, n = 37 and r = 2. 0 vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the Find a . minimum number of pages she needs to read per day 37 to finish the book by the end of her vacation? SOLUTION: The number of pages to be read is 800 – 112 or 688. The minimum number of pages to read per day is The thickness would be about 13,744 km. . ANSWER: about 13,744 km ANSWER: 86 pg/day 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is SOLUTION: currently valued at $24,000, to the nearest dollar, Sample answer: The consecutive terms do not share how much will it be worth in 6 years? a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in ANSWER: then evaluate. Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a The worth of the car will be about $9052 after 6 years. common difference of 8. SOLUTION: ANSWER: Sample answer: A babysitter earns $20 for cleaning $9052 the house and $8 extra for every hour she watches the children. 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of ANSWER: paper that is 0.1 mm thick could be folded 37 times, Sample answer: A babysitter earns $20 for cleaning how thick would it be? the house and $8 extra for every hour she watches the children. SOLUTION: Given a = 0.1, n = 37 and r = 2. 0 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the Find a . terms is –42. Find the terms. 37 SOLUTION: Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. The thickness would be about 13,744 km. ANSWER: about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. Sample answer: SOLUTION: Let d = 5. Sample answer: The consecutive terms do not share Therefore, the terms are –3, 2, 7. a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. ANSWER: –3, 2, 7 ANSWER: 57. ERROR ANALYSIS Brody and Gen are Sample answer: The consecutive terms do not share determining whether the sequence 8, 8, 8,… is a common difference. For instance, 22 – 17 = 5, arithmetic, geometric, neither, or both. Is either of while 17 – 13 = 4. them correct? Explain your reasoning. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. SOLUTION: Sample answer: Neither; the sequence is both 56. CHALLENGE The sum of three consecutive terms arithmetic and geometric. of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: ANSWER: Let x be the first term in the arithmetic sequence. Sample answer: Neither; the sequence is both Therefore, the next two terms should be x + d and x arithmetic and geometric. + 2d. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: –3, 2, 7 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Yes 3. 1, 2, 4, 8, 16 SOLUTION: Subtract each term from the term directly after it. Determine whether each sequence is arithmetic no. There is no common difference. 1. 8, –2, –12, –22 Therefore, the sequence is not arithmetic. SOLUTION: ANSWER: Subtract each term from the term directly after it. No 4. 0.6, 0.9, 1.2, 1.8, ... The common difference is –10. Therefore, the sequence is arithmetic. SOLUTION: Subtract each term from the term directly after it. ANSWER: Yes There is no common difference. 2. –19, –12, –5, 2, 9 Therefore, the sequence is not arithmetic. SOLUTION: ANSWER: Subtract each term from the term directly after it. No Find the next four terms of each arithmetic sequence. Then graph the sequence. The common difference is 7. Therefore, the sequence is arithmetic. 5. 6, 18, 30, … SOLUTION: ANSWER: Subtract each term from the term directly after it. Yes 3. 1, 2, 4, 8, 16 The common difference is 12. SOLUTION: Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the next term, add 12 to the last term. 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 There is no common difference. 66 + 12 = 78 Therefore, the sequence is not arithmetic. Graph the sequence. ANSWER: No 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: Subtract each term from the term directly after it. ANSWER: 42, 54, 66, 78 There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No Find the next four terms of each arithmetic sequence. Then graph the sequence. 5. 6, 18, 30, … 6. 15, 6, –3, … SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is 12. Therefore, the sequence is arithmetic. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. 30 + 12 = 42 To find the next term, add –9 to the last term. 42 + 12 = 54 54 + 12 = 66 –3 + (–9) = –12 66 + 12 = 78 –12 + (–9) = –21 –21 + (–9) = –30 Graph the sequence. –30 + (–9) = –39 Graph the sequence. ANSWER: 42, 54, 66, 78 ANSWER: –12, –21, –30, –39 7. –19, –11, –3, … 6. 15, 6, –3, … SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is 8. The common difference is –9. Therefore, the sequence is arithmetic. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. To find the next term, add –9 to the last term. –3 + 8 = 5 –3 + (–9) = –12 5 + 8 = 13 –12 + (–9) = –21 13 + 8 = 21 –21 + (–9) = –30 21 + 8 = 29 –30 + (–9) = –39 Graph the sequence. Graph the sequence. ANSWER: ANSWER: 5, 13, 21, 29 –12, –21, –30, –39 10-1 Sequences as Functio ns 7. –19, –11, –3, … 8. –26, –33, –40, … SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is 8. The common difference is –7. Therefore, the sequence is arithmetic. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. To find the next term, add –7 to the last term. –3 + 8 = 5 –40 + (–7) = –47 5 + 8 = 13 –47 + (–7) = –54 13 + 8 = 21 –54 + (–7) = –61 21 + 8 = 29 –61 + (–7) = –68 Graph the sequence. Graph the sequence. ANSWER: ANSWER: 5, 13, 21, 29 –47, –54, –61, –68 8. –26, –33, –40, … 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. SOLUTION: Subtract each term from the term directly after it. a. How much will Kelly have saved after 8 weeks? b. If the car costs $2000, how long will it take her to eSolutionsManual-PoweredbyCognero save enough money at this rate? Page3 The common difference is –7. Therefore, the sequence is arithmetic. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 To find the next term, add –7 to the last term. After 8 weeks, she will have 250 + (8 × 75) or $850. –40 + (–7) = –47 b. Given a = 2000. –47 + (–7) = –54 n –54 + (–7) = –61 –61 + (–7) = –68 Find n. Graph the sequence. So, it will take about 24 weeks to save $2000. ANSWER: a. $850 b. 24 wk ANSWER: –47, –54, –61, –68 Determine whether each sequence is geometric. Write yes or no. 10. –8, –5, –1, 4, … SOLUTION: Find the ratio of the consecutive terms. 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to Since the ratios are not same, the sequence is not save $75 per week from her job as a waitress. geometric. a. How much will Kelly have saved after 8 weeks? ANSWER: No b. If the car costs $2000, how long will it take her to save enough money at this rate? 11. 4, 12, 36, 108, … SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 SOLUTION: After 8 weeks, she will have 250 + (8 × 75) or $850. Find the ratio of the consecutive terms. b. Given a = 2000. n Find n. Since the ratios are the same, the sequence is geometric. ANSWER: Yes So, it will take about 24 weeks to save $2000. 12. 27, 9, 3, 1, … ANSWER: a. $850 SOLUTION: b. 24 wk Find the ratio of the consecutive terms. Determine whether each sequence is geometric. Write yes or no. Since the ratios are the same, the sequence is 10. –8, –5, –1, 4, … geometric. SOLUTION: ANSWER: Find the ratio of the consecutive terms. Yes 13. 7, 14, 21, 28, … Since the ratios are not same, the sequence is not SOLUTION: geometric. Find the ratio of the consecutive terms. ANSWER: No Since the ratios are not the same, the sequence is not geometric. 11. 4, 12, 36, 108, … SOLUTION: ANSWER: Find the ratio of the consecutive terms. No Find the next three terms of each geometric sequence. Then graph the sequence. Since the ratios are the same, the sequence is 14. 8, 12, 18, 27, … geometric. SOLUTION: ANSWER: Find the ratio of the consecutive terms. Yes 12. 27, 9, 3, 1, … Since the ratios are the same, the sequence is SOLUTION: geometric Find the ratio of the consecutive terms. To find the next term, multiply the previous term by . Since the ratios are the same, the sequence is geometric. ANSWER: Yes 13. 7, 14, 21, 28, … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. ANSWER: ANSWER: No 40.5, 60.75, 91.125 Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … SOLUTION: Find the ratio of the consecutive terms. 15. 8, 16, 32, 64, … Since the ratios are the same, the sequence is geometric SOLUTION: Find the ratio of the consecutive terms. To find the next term, multiply the previous term by . Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: 40.5, 60.75, 91.125 ANSWER: 128, 256, 512 15. 8, 16, 32, 64, … SOLUTION: 16. 250, 50, 10, 2, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are the same, the sequence is To find the next term, multiply the previous term by geometric 2. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric 17. 9, –3, 1, , … To find the next term, multiply the previous term by . SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Graph the sequence. To find the next term, multiply the previous term by . Graph the sequence. ANSWER: ANSWER: 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is Determine whether each sequence is geometric. arithmetic, geometric, or neither. Explain your reasoning. To find the next term, multiply the previous term by 18. 5, 1, 7, 3, 9, … . SOLUTION: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not the same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … ANSWER: SOLUTION: To find the common difference, subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. The common ratio is . 18. 5, 1, 7, 3, 9, … Since the ratios are the same, the sequence is geometric. SOLUTION: ANSWER: Geometric; the common ratio is . There is no common difference. Therefore, the sequence is not arithmetic. 20. 12, 16, 20, 24, … Find the ratio of the consecutive terms. SOLUTION: To find the common difference, subtract any term from the term directly after it. Since the ratios are not the same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. The common difference is 4. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. Since the ratios are not the same, the sequence is not geometric. ANSWER: Arithmetic; the common difference is 4. There is no common difference. Therefore, the sequence is not arithmetic. Determine whether each sequence is Find the ratio of the consecutive terms. arithmetic. Write yes or no. 21. The common ratio is . SOLUTION: Subtract any term from the term directly after it. Since the ratios are the same, the sequence is geometric. ANSWER: Geometric; the common ratio is . There is no common difference. Therefore, the sequence is not arithmetic. 20. 12, 16, 20, 24, … ANSWER: SOLUTION: No To find the common difference, subtract any term from the term directly after it. 22. –9, –3, 0, 3, 9 SOLUTION: The common difference is 4. Subtract any term from the term directly after it. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. Since the ratios are not the same, the sequence is not geometric. ANSWER: No ANSWER: Arithmetic; the common difference is 4. 23. 14, –5, –19, … SOLUTION: Determine whether each sequence is arithmetic. Write yes or no. Subtract any term from the term directly after it. 21. There is no common difference. SOLUTION: Therefore, the sequence is not arithmetic. Subtract any term from the term directly after it. ANSWER: No 24. There is no common difference. Therefore, the sequence is not arithmetic. SOLUTION: Subtract any term from the term directly after it. ANSWER: No 22. –9, –3, 0, 3, 9 SOLUTION: The common difference is . Subtract any term from the term directly after it. Therefore, the sequence is arithmetic. ANSWER: Yes There is no common difference. Therefore, the sequence is not arithmetic. Find the next four terms of each arithmetic sequence. Then graph the sequence. ANSWER: No 25. –4, –1, 2, 5,… 23. 14, –5, –19, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. There is no common difference. To find the next term, add 3 to the last term. Therefore, the sequence is not arithmetic. 5 + 3 = 8 ANSWER: 8 + 3 = 11 11 + 3 = 14 No 14 + 3 = 17 Graph the sequence. 24. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is . 8, 11, 14, 17 Therefore, the sequence is arithmetic. ANSWER: Yes Find the next four terms of each arithmetic sequence. Then graph the sequence. 25. –4, –1, 2, 5,… SOLUTION: 26. 10, 2, –6, –14, … Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. To find the next term, add 3 to the last term. The common difference is –8. Therefore, this sequence is arithmetic. 5 + 3 = 8 8 + 3 = 11 To find the next term, add –8 to the last term. 11 + 3 = 14 14 + 3 = 17 –14 + (–8) = –22 –22 + (–8) = –30 Graph the sequence. –30 + (–8) = –38 –38 + (–8) = –46 Graph the sequence. ANSWER: 8, 11, 14, 17 ANSWER: –22, –30, –38, – 46 26. 10, 2, –6, –14, … 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. The common difference is –6. To find the next term, add –8 to the last term. Therefore, the sequence is arithmetic. –14 + (–8) = –22 To find the next term, add –6 to the last term. –22 + (–8) = –30 –30 + (–8) = –38 –23 + (–6) = –29 –38 + (–8) = –46 –29 + (–6) = –35 –35 + (–6) = –41 Graph the sequence. –41 + (–6) = –47 Graph the sequence. ANSWER: –22, –30, –38, – 46 ANSWER: –29, –35, – 41, – 47 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. 28. –19, –2, 15, … SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. The common difference is 17. –23 + (–6) = –29 Therefore, the sequence is arithmetic. –29 + (–6) = –35 –35 + (–6) = –41 To find the next term, add 17 to the last term. –41 + (–6) = –47 15 + 17 = 32 Graph the sequence. 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 Graph the sequence. ANSWER: –29, –35, – 41, – 47 ANSWER: 32, 49, 66, 83 28. –19, –2, 15, … SOLUTION: 29. Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 32 + 17 = 49 The common difference is . 49 + 17 = 66 66 + 17 = 83 Therefore, the sequence is arithmetic. Graph the sequence. To find the next term, add to the last term. ANSWER: Graph the sequence. 32, 49, 66, 83 ANSWER: 29. SOLUTION: Subtract any term from the term directly after it. The common difference is . Therefore, the sequence is arithmetic. 30. To find the next term, add to the last term. SOLUTION: Subtract any term from the term directly after it. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 30. SOLUTION: Subtract any term from the term directly after it. The common difference is –1. 31. THEATER There are 28 seats in the front row of a Therefore, the sequence is arithmetic. theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? To find the next term, add −1 to the last term. SOLUTION: Given a = 28, d = 2 and n = 24. 1 Find a . 24 Graph the sequence. ANSWER: 74 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? ANSWER: b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue indefinitely? Explain. SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Find a . 18 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, Therefore he will row for 30 minutes and 30 seconds how many seats are in the last row of the theater? on the 38th day. b. Given a = 5, d = 1.5 and a = 60. SOLUTION: 1 n Find n. Given a = 28, d = 2 and n = 24. 1 Find a . 24 Mario will first row an hour or more on the 38th day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be ANSWER: dedicated to rowing. 74 ANSWER: 32. CCSS SENSE-MAKING Mario began an exercise a. 30 minutes and 30 seconds program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and b. on the 38th day increase his rowing time by one minute and thirty seconds each day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be a. How long will he row on the 18th day? dedicated to rowing. b. On what day will Mario first row an hour or more? Determine whether each sequence is geometric. Write yes or no. c. Is it reasonable for this pattern to continue indefinitely? Explain. 33. 21, 14, 7, … SOLUTION: a. Given a = 5, d = 1.5 and n = 18. SOLUTION: 1 Find the ratio of the consecutive terms. Find a . 18 Since the ratios are not the same, the sequence is not geometric. Therefore he will row for 30 minutes and 30 seconds on the 38th day. ANSWER: b. Given a = 5, d = 1.5 and a = 60. No 1 n Find n. 34. 124, 186, 248, … SOLUTION: Find the ratio of the consecutive terms. Mario will first row an hour or more on the 38th day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be Since the ratios are not the same, the sequence is not dedicated to rowing. geometric. ANSWER: ANSWER: a. 30 minutes and 30 seconds No b. on the 38th day 35. –27, 18, –12, … c. Sample answer: It is unreasonable because there SOLUTION: are only so many hours in the day that can be dedicated to rowing. Find the ratio of the consecutive terms. Determine whether each sequence is Since the ratios are the same, the sequence is geometric. Write yes or no. geometric. 33. 21, 14, 7, … ANSWER: Yes 36. 162, 108, 72, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Since the ratios are same, the sequence is geometric. ANSWER: ANSWER: No Yes 34. 124, 186, 248, … 37. SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. ANSWER: No 35. –27, 18, –12, … SOLUTION: Since the ratios are not same, the sequence is not Find the ratio of the consecutive terms. geometric. ANSWER: Since the ratios are the same, the sequence is No geometric. ANSWER: 38. –4, –2, 0, 2, … Yes 36. 162, 108, 72, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are same, the sequence is geometric. ANSWER: No ANSWER: Yes Find the next three terms of the sequence. Then graph the sequence. 37. 39. 0.125, –0.5, 2, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. Since the ratios are not same, the sequence is not geometric. Graph the sequence. ANSWER: No 38. –4, –2, 0, 2, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are not same, the sequence is not – 8, 32, –128 geometric. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: 40. 18, 12, 8, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: – 8, 32, –128 ANSWER: 40. 18, 12, 8, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. 41. 64, 48, 36, … To find the next term, multiply the previous term by SOLUTION: . Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 41. 64, 48, 36, … SOLUTION: Find the ratio of the consecutive terms. 42. 81, 108, 144, … Since the ratios are same, the sequence is geometric. SOLUTION: To find the next term, multiply the previous term by Find the ratio of the consecutive terms. . Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. 43. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by SOLUTION: . Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 27, 81, 243 43. SOLUTION: Find the ratio of the consecutive terms. 44. 1, 0.1, 0.01, 0.001, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. Graph the sequence. Graph the sequence. ANSWER: 27, 81, 243 ANSWER: 0.0001, 0.00001, 0.000001 44. 1, 0.1, 0.01, 0.001, … SOLUTION: Determine whether each sequence is Find the ratio of the consecutive terms. arithmetic, geometric, or neither. Explain your reasoning. 45. 3, 12, 27, 48, … Since the ratios are same, the sequence is geometric. SOLUTION: To find the next term, multiply the previous term by Subtract each term from the term directly after it. 0.1. There is no common difference. Graph the sequence. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. ANSWER: 0.0001, 0.00001, 0.000001 46. 1, –2, –5, –8, … SOLUTION: Subtract each term from the term directly after it. The common difference is –3. Therefore, the sequence is arithmetic. Determine whether each sequence is To find the common ratio, find the ratio of the arithmetic, geometric, or neither. Explain your consecutive terms. reasoning. 45. 3, 12, 27, 48, … SOLUTION: Since the ratios are not same, the sequence is not Subtract each term from the term directly after it. geometric. ANSWER: Arithmetic; the common difference is –3. There is no common difference. 47. 12, 36, 108, 324, … Therefore, the sequence is not arithmetic. SOLUTION: To find the common ratio, find the ratio of the consecutive terms. Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not There is no common difference. geometric. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the ANSWER: consecutive terms. Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … The common ratio is 3. SOLUTION: Since the ratios are same, the sequence is geometric. Subtract each term from the term directly after it. ANSWER: Geometric; the common ratio is 3. The common difference is –3. Therefore, the sequence is arithmetic. 48. To find the common ratio, find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not geometric. ANSWER: There is no common difference. Arithmetic; the common difference is –3. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the 47. 12, 36, 108, 324, … consecutive terms. SOLUTION: Subtract each term from the term directly after it. The common ratio is . There is no common difference. Since the ratios are the same, the sequence is Therefore, this sequence is not arithmetic. geometric. To find the common ratio, find the ratio of the consecutive terms. ANSWER: Geometric; the common ratio is . The common ratio is 3. 49. Since the ratios are same, the sequence is geometric. SOLUTION: ANSWER: Subtract each term from the term directly after it. Geometric; the common ratio is 3. 48. The common difference is . SOLUTION: Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, this sequence is not arithmetic. Since the ratios are not same, the sequence is not To find the common ratio, find the ratio of the geometric. consecutive terms. ANSWER: Arithmetic; the common difference is . The common ratio is . 50. 6, 9, 14, 21, … Since the ratios are the same, the sequence is geometric. SOLUTION: Subtract each term from the term directly after it. ANSWER: Geometric; the common ratio is . There is no common difference. Therefore, the sequence is not arithmetic. 49. To find the common ratio, find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. The common difference is . Therefore, the sequence is arithmetic. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is To find the common ratio, find the ratio of the consecutive terms. going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation? SOLUTION: The number of pages to be read is 800 – 112 or 688. Since the ratios are not same, the sequence is not geometric. The minimum number of pages to read per day is . ANSWER: Arithmetic; the common difference is . ANSWER: 86 pg/day 50. 6, 9, 14, 21, … 52. DEPRECIATION Tammy’s car is expected to SOLUTION: depreciate at a rate of 15% per year. If her car is Subtract each term from the term directly after it. currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in There is no common difference. Therefore, the sequence is not arithmetic. then evaluate. To find the common ratio, find the ratio of the consecutive terms. The worth of the car will be about $9052 after 6 years. Since the ratios are not same, the sequence is not geometric. ANSWER: $9052 ANSWER: Neither; there is no common difference or ratio. 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, 51. READING Sareeta took an 800-page book on how thick would it be? vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day SOLUTION: to finish the book by the end of her vacation? Given a = 0.1, n = 37 and r = 2. 0 SOLUTION: Find a . 37 The number of pages to be read is 800 – 112 or 688. The minimum number of pages to read per day is . The thickness would be about 13,744 km. ANSWER: 86 pg/day ANSWER: about 13,744 km 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, 54. REASONING Explain why the sequence 8, 10, 13, how much will it be worth in 6 years? 17, 22 is not arithmetic. SOLUTION: SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, then evaluate. while 17 – 13 = 4. ANSWER: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, The worth of the car will be about $9052 after 6 while 17 – 13 = 4. years. 55. OPEN ENDED Describe a real-life situation that ANSWER: can be represented by an arithmetic sequence with a $9052 common difference of 8. 53. CCSS REGULARITY When a piece of paper is SOLUTION: folded onto itself, it doubles in thickness. If a piece of Sample answer: A babysitter earns $20 for cleaning paper that is 0.1 mm thick could be folded 37 times, the house and $8 extra for every hour she watches how thick would it be? the children. SOLUTION: ANSWER: Given a = 0.1, n = 37 and r = 2. Sample answer: A babysitter earns $20 for cleaning 0 the house and $8 extra for every hour she watches the children. Find a . 37 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: Let x be the first term in the arithmetic sequence. The thickness would be about 13,744 km. Therefore, the next two terms should be x + d and x + 2d. ANSWER: about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. SOLUTION: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: Sample answer: The consecutive terms do not share ANSWER: a common difference. For instance, 22 – 17 = 5, –3, 2, 7 while 17 – 13 = 4. 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is 55. OPEN ENDED Describe a real-life situation that arithmetic, geometric, neither, or both. Is either of can be represented by an arithmetic sequence with a them correct? Explain your reasoning. common difference of 8. SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: SOLUTION: Sample answer: Neither; the sequence is both Let x be the first term in the arithmetic sequence. arithmetic and geometric. Therefore, the next two terms should be x + d and x + 2d. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: –3, 2, 7 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Determine whether each sequence is arithmetic no. Yes 1. 8, –2, –12, –22 3. 1, 2, 4, 8, 16 SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: Yes ANSWER: No 2. –19, –12, –5, 2, 9 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: Yes ANSWER: No 3. 1, 2, 4, 8, 16 Find the next four terms of each arithmetic sequence. Then graph the sequence. SOLUTION: Subtract each term from the term directly after it. 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: The common difference is 12. No Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. 4. 0.6, 0.9, 1.2, 1.8, ... 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 SOLUTION: 66 + 12 = 78 Subtract each term from the term directly after it. Graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No Find the next four terms of each arithmetic sequence. Then graph the sequence. ANSWER: 42, 54, 66, 78 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. The common difference is 12. Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. 6. 15, 6, –3, … 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 SOLUTION: 66 + 12 = 78 Subtract each term from the term directly after it. Graph the sequence. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add –9 to the last term. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 ANSWER: Graph the sequence. 42, 54, 66, 78 ANSWER: –12, –21, –30, –39 6. 15, 6, –3, … SOLUTION: Subtract each term from the term directly after it. The common difference is –9. Therefore, the sequence is arithmetic. 7. –19, –11, –3, … To find the next term, add –9 to the last term. SOLUTION: Subtract each term from the term directly after it. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 Graph the sequence. The common difference is 8. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. ANSWER: –12, –21, –30, –39 ANSWER: 5, 13, 21, 29 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. The common difference is 8. Therefore, the sequence is arithmetic. 8. –26, –33, –40, … To find the next term, add 8 to the last term. SOLUTION: –3 + 8 = 5 Subtract each term from the term directly after it. 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. The common difference is –7. Therefore, the sequence is arithmetic. To find the next term, add –7 to the last term. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 –61 + (–7) = –68 Graph the sequence. ANSWER: 5, 13, 21, 29 ANSWER: –47, –54, –61, –68 8. –26, –33, –40, … SOLUTION: Subtract each term from the term directly after it. The common difference is –7. Therefore, the sequence is arithmetic. 9. FINANCIAL LITERACY Kelly is saving her To find the next term, add –7 to the last term. money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. –40 + (–7) = –47 –47 + (–7) = –54 a. How much will Kelly have saved after 8 weeks? –54 + (–7) = –61 –61 + (–7) = –68 b. If the car costs $2000, how long will it take her to save enough money at this rate? Graph the sequence. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. b. Given a = 2000. n Find n. ANSWER: –47, –54, –61, –68 So, it will take about 24 weeks to save $2000. ANSWER: a. $850 10-1 Sequences as Functio ns b. 24 wk 9. FINANCIAL LITERACY Kelly is saving her Determine whether each sequence is money to buy a car. She has $250, and she plans to geometric. Write yes or no. save $75 per week from her job as a waitress. 10. –8, –5, –1, 4, … a. How much will Kelly have saved after 8 weeks? SOLUTION: b. If the car costs $2000, how long will it take her to Find the ratio of the consecutive terms. save enough money at this rate? SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 Since the ratios are not same, the sequence is not After 8 weeks, she will have 250 + (8 × 75) or $850. geometric. b. Given a = 2000. n ANSWER: Find n. No 11. 4, 12, 36, 108, … SOLUTION: So, it will take about 24 weeks to save $2000. Find the ratio of the consecutive terms. ANSWER: a. $850 Since the ratios are the same, the sequence is b. 24 wk geometric. Determine whether each sequence is ANSWER: geometric. Write yes or no. Yes 10. –8, –5, –1, 4, … 12. 27, 9, 3, 1, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are the same, the sequence is geometric. ANSWER: No ANSWER: eSolutionsManual-PoweredbyCognero Yes Page4 11. 4, 12, 36, 108, … 13. 7, 14, 21, 28, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are not the same, the sequence is not geometric. ANSWER: ANSWER: Yes No 12. 27, 9, 3, 1, … Find the next three terms of each geometric sequence. Then graph the sequence. SOLUTION: Find the ratio of the consecutive terms. 14. 8, 12, 18, 27, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Since the ratios are the same, the sequence is Yes geometric To find the next term, multiply the previous term by 13. 7, 14, 21, 28, … . SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Graph the sequence. ANSWER: No Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: 40.5, 60.75, 91.125 Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 2. ANSWER: 40.5, 60.75, 91.125 Graph the sequence. ANSWER: 15. 8, 16, 32, 64, … 128, 256, 512 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 2. 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . ANSWER: 128, 256, 512 Graph the sequence. 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . 17. 9, –3, 1, , … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 18. 5, 1, 7, 3, 9, … Graph the sequence. SOLUTION: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. ANSWER: Since the ratios are not the same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 18. 5, 1, 7, 3, 9, … There is no common difference. Therefore, the sequence is not arithmetic. SOLUTION: Find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. The common ratio is . Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are not the same, the sequence is not ANSWER: geometric. Geometric; the common ratio is . ANSWER: Neither; there is no common difference or ratio. 20. 12, 16, 20, 24, … 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. SOLUTION: To find the common difference, subtract any term from the term directly after it. The common difference is 4. Therefore, the sequence is arithmetic. There is no common difference. Find the ratio of the consecutive terms. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. The common ratio is . ANSWER: Arithmetic; the common difference is 4. Since the ratios are the same, the sequence is geometric. Determine whether each sequence is arithmetic. Write yes or no. ANSWER: Geometric; the common ratio is . 21. 20. 12, 16, 20, 24, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: To find the common difference, subtract any term from the term directly after it. There is no common difference. The common difference is 4. Therefore, the sequence is not arithmetic. Therefore, the sequence is arithmetic. ANSWER: Find the ratio of the consecutive terms. No 22. –9, –3, 0, 3, 9 Since the ratios are not the same, the sequence is not geometric. SOLUTION: Subtract any term from the term directly after it. ANSWER: Arithmetic; the common difference is 4. Determine whether each sequence is There is no common difference. arithmetic. Write yes or no. Therefore, the sequence is not arithmetic. 21. ANSWER: No SOLUTION: Subtract any term from the term directly after it. 23. 14, –5, –19, … SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No ANSWER: No 22. –9, –3, 0, 3, 9 24. SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No The common difference is . Therefore, the sequence is arithmetic. 23. 14, –5, –19, … ANSWER: SOLUTION: Yes Subtract any term from the term directly after it. Find the next four terms of each arithmetic sequence. Then graph the sequence. 25. –4, –1, 2, 5,… There is no common difference. Therefore, the sequence is not arithmetic. SOLUTION: Subtract any term from the term directly after it. ANSWER: No 24. The common difference is 3. Therefore, the sequence is arithmetic. SOLUTION: To find the next term, add 3 to the last term. Subtract any term from the term directly after it. 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 14 + 3 = 17 Graph the sequence. The common difference is . Therefore, the sequence is arithmetic. ANSWER: Yes Find the next four terms of each arithmetic sequence. Then graph the sequence. ANSWER: 25. –4, –1, 2, 5,… 8, 11, 14, 17 SOLUTION: Subtract any term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. To find the next term, add 3 to the last term. 26. 10, 2, –6, –14, … 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 SOLUTION: 14 + 3 = 17 Subtract any term from the term directly after it. Graph the sequence. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. –14 + (–8) = –22 –22 + (–8) = –30 –30 + (–8) = –38 –38 + (–8) = –46 ANSWER: 8, 11, 14, 17 Graph the sequence. ANSWER: 26. 10, 2, –6, –14, … –22, –30, –38, – 46 SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. 27. –5, –11, –17, –23, … –14 + (–8) = –22 –22 + (–8) = –30 –30 + (–8) = –38 SOLUTION: –38 + (–8) = –46 Subtract any term from the term directly after it. Graph the sequence. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. –23 + (–6) = –29 –29 + (–6) = –35 –35 + (–6) = –41 –41 + (–6) = –47 ANSWER: Graph the sequence. –22, –30, –38, – 46 27. –5, –11, –17, –23, … ANSWER: –29, –35, – 41, – 47 SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. –23 + (–6) = –29 –29 + (–6) = –35 28. –19, –2, 15, … –35 + (–6) = –41 –41 + (–6) = –47 SOLUTION: Subtract any term from the term directly after it. Graph the sequence. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 ANSWER: –29, –35, – 41, – 47 Graph the sequence. ANSWER: 28. –19, –2, 15, … 32, 49, 66, 83 SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 29. 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 SOLUTION: Subtract any term from the term directly after it. Graph the sequence. The common difference is . Therefore, the sequence is arithmetic. To find the next term, add to the last term. ANSWER: 32, 49, 66, 83 Graph the sequence. 29. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is . Therefore, the sequence is arithmetic. To find the next term, add to the last term. 30. SOLUTION: Graph the sequence. Subtract any term from the term directly after it. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. ANSWER: Graph the sequence. 30. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? Graph the sequence. SOLUTION: Given a = 28, d = 2 and n = 24. 1 Find a . 24 ANSWER: ANSWER: 74 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue 31. THEATER There are 28 seats in the front row of a indefinitely? Explain. theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 SOLUTION: Given a1 = 28, d = 2 and n = 24. Find a18. Find a . 24 Therefore he will row for 30 minutes and 30 seconds on the 38th day. b. Given a = 5, d = 1.5 and a = 60. 1 n ANSWER: Find n. 74 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty Mario will first row an hour or more on the 38th day. seconds each day. c. Sample answer: It is unreasonable because there a. How long will he row on the 18th day? are only so many hours in the day that can be dedicated to rowing. b. On what day will Mario first row an hour or more? ANSWER: c. Is it reasonable for this pattern to continue a. 30 minutes and 30 seconds indefinitely? Explain. b. on the 38th day SOLUTION: c. Sample answer: It is unreasonable because there a. Given a = 5, d = 1.5 and n = 18. 1 are only so many hours in the day that can be dedicated to rowing. Find a . 18 Determine whether each sequence is geometric. Write yes or no. 33. 21, 14, 7, … Therefore he will row for 30 minutes and 30 seconds on the 38th day. SOLUTION: b. Given a = 5, d = 1.5 and a = 60. 1 n Find the ratio of the consecutive terms. Find n. Since the ratios are not the same, the sequence is not geometric. Mario will first row an hour or more on the 38th day. ANSWER: c. Sample answer: It is unreasonable because there No are only so many hours in the day that can be dedicated to rowing. 34. 124, 186, 248, … ANSWER: a. 30 minutes and 30 seconds SOLUTION: Find the ratio of the consecutive terms. b. on the 38th day c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing. Since the ratios are not the same, the sequence is not geometric. Determine whether each sequence is geometric. Write yes or no. ANSWER: No 33. 21, 14, 7, … 35. –27, 18, –12, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are not the same, the sequence is not geometric. ANSWER: Yes ANSWER: 36. 162, 108, 72, … No SOLUTION: Find the ratio of the consecutive terms. 34. 124, 186, 248, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. ANSWER: Yes Since the ratios are not the same, the sequence is not geometric. 37. ANSWER: No SOLUTION: Find the ratio of the consecutive terms. 35. –27, 18, –12, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Yes 36. 162, 108, 72, … Since the ratios are not same, the sequence is not geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: No Since the ratios are same, the sequence is geometric. 38. –4, –2, 0, 2, … SOLUTION: ANSWER: Find the ratio of the consecutive terms. Yes 37. Since the ratios are not same, the sequence is not geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are same, the sequence is geometric ANSWER: No To find the next term, multiply the previous term with −4. 38. –4, –2, 0, 2, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. ANSWER: 39. 0.125, –0.5, 2, … – 8, 32, –128 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. 40. 18, 12, 8, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: – 8, 32, –128 Graph the sequence. 40. 18, 12, 8, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . 41. 64, 48, 36, … SOLUTION: Graph the sequence. Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 41. 64, 48, 36, … SOLUTION: ANSWER: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 42. 81, 108, 144, … SOLUTION: ANSWER: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . 43. SOLUTION: Graph the sequence. Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. ANSWER: Graph the sequence. 43. ANSWER: 27, 81, 243 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. 44. 1, 0.1, 0.01, 0.001, … SOLUTION: Graph the sequence. Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. ANSWER: Graph the sequence. 27, 81, 243 ANSWER: 44. 1, 0.1, 0.01, 0.001, … 0.0001, 0.00001, 0.000001 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. Graph the sequence. 45. 3, 12, 27, 48, … SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the ANSWER: consecutive terms. 0.0001, 0.00001, 0.000001 Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … Determine whether each sequence is arithmetic, geometric, or neither. Explain your SOLUTION: reasoning. Subtract each term from the term directly after it. 45. 3, 12, 27, 48, … SOLUTION: Subtract each term from the term directly after it. The common difference is –3. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the Since the ratios are not same, the sequence is not consecutive terms. geometric. ANSWER: Arithmetic; the common difference is –3. Since the ratios are not same, the sequence is not geometric. 47. 12, 36, 108, 324, … ANSWER: SOLUTION: Neither; there is no common difference or ratio. Subtract each term from the term directly after it. 46. 1, –2, –5, –8, … SOLUTION: There is no common difference. Subtract each term from the term directly after it. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common difference is –3. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the The common ratio is 3. consecutive terms. Since the ratios are same, the sequence is geometric. ANSWER: Geometric; the common ratio is 3. Since the ratios are not same, the sequence is not geometric. ANSWER: 48. Arithmetic; the common difference is –3. SOLUTION: 47. 12, 36, 108, 324, … Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, this sequence is not arithmetic. There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. To find the common ratio, find the ratio of the consecutive terms. The common ratio is . The common ratio is 3. Since the ratios are the same, the sequence is Since the ratios are same, the sequence is geometric. geometric. ANSWER: ANSWER: Geometric; the common ratio is 3. Geometric; the common ratio is . 48. 49. SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. There is no common difference. Therefore, this sequence is not arithmetic. The common difference is . To find the common ratio, find the ratio of the consecutive terms. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common ratio is . Since the ratios are the same, the sequence is Since the ratios are not same, the sequence is not geometric. geometric. ANSWER: ANSWER: Geometric; the common ratio is . Arithmetic; the common difference is . 50. 6, 9, 14, 21, … 49. SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the The common difference is . consecutive terms. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. Since the ratios are not same, the sequence is not geometric. 51. READING Sareeta took an 800-page book on ANSWER: vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the Arithmetic; the common difference is . minimum number of pages she needs to read per day to finish the book by the end of her vacation? 50. 6, 9, 14, 21, … SOLUTION: The number of pages to be read is 800 – 112 or 688. SOLUTION: The minimum number of pages to read per day is Subtract each term from the term directly after it. . There is no common difference. ANSWER: Therefore, the sequence is not arithmetic. 86 pg/day To find the common ratio, find the ratio of the consecutive terms. 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? Since the ratios are not same, the sequence is not SOLUTION: geometric. Substitute 0.15, 6 and 24000 for r, t and P in then evaluate. ANSWER: Neither; there is no common difference or ratio. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is The worth of the car will be about $9052 after 6 going to be on vacation for 8 days, what is the years. minimum number of pages she needs to read per day to finish the book by the end of her vacation? ANSWER: $9052 SOLUTION: The number of pages to be read is 800 – 112 or 688. 53. CCSS REGULARITY When a piece of paper is The minimum number of pages to read per day is folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, . how thick would it be? SOLUTION: ANSWER: Given a0 = 0.1, n = 37 and r = 2. 86 pg/day Find a . 37 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? SOLUTION: The thickness would be about 13,744 km. Substitute 0.15, 6 and 24000 for r, t and P in then evaluate. ANSWER: about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. The worth of the car will be about $9052 after 6 years. SOLUTION: Sample answer: The consecutive terms do not share ANSWER: a common difference. For instance, 22 – 17 = 5, $9052 while 17 – 13 = 4. 53. CCSS REGULARITY When a piece of paper is ANSWER: folded onto itself, it doubles in thickness. If a piece of Sample answer: The consecutive terms do not share paper that is 0.1 mm thick could be folded 37 times, a common difference. For instance, 22 – 17 = 5, how thick would it be? while 17 – 13 = 4. SOLUTION: 55. OPEN ENDED Describe a real-life situation that Given a = 0.1, n = 37 and r = 2. 0 can be represented by an arithmetic sequence with a common difference of 8. Find a . 37 SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. The thickness would be about 13,744 km. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches ANSWER: the children. about 13,744 km 56. CHALLENGE The sum of three consecutive terms 54. REASONING Explain why the sequence 8, 10, 13, of an arithmetic sequence is 6. The product of the 17, 22 is not arithmetic. terms is –42. Find the terms. SOLUTION: SOLUTION: Let x be the first term in the arithmetic sequence. Sample answer: The consecutive terms do not share Therefore, the next two terms should be x + d and x a common difference. For instance, 22 – 17 = 5, + 2d. while 17 – 13 = 4. ANSWER: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. Sample answer: Let d = 5. SOLUTION: Therefore, the terms are –3, 2, 7. Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches ANSWER: the children. –3, 2, 7 57. ERROR ANALYSIS Brody and Gen are ANSWER: determining whether the sequence 8, 8, 8,… is Sample answer: A babysitter earns $20 for cleaning arithmetic, geometric, neither, or both. Is either of the house and $8 extra for every hour she watches them correct? Explain your reasoning. the children. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. Sample answer: ANSWER: Let d = 5. Sample answer: Neither; the sequence is both Therefore, the terms are –3, 2, 7. arithmetic and geometric. ANSWER: –3, 2, 7 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither 57. ERROR ANALYSIS Brody and Gen are geometric nor arithmetic that begins 3, 9,… . determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Yes 3. 1, 2, 4, 8, 16 SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. Determine whether each sequence is arithmetic ANSWER: no. No 1. 8, –2, –12, –22 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: Yes ANSWER: No 2. –19, –12, –5, 2, 9 Find the next four terms of each arithmetic sequence. Then graph the sequence. SOLUTION: Subtract each term from the term directly after it. 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: The common difference is 12. Yes Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. 3. 1, 2, 4, 8, 16 30 + 12 = 42 42 + 12 = 54 SOLUTION: 54 + 12 = 66 Subtract each term from the term directly after it. 66 + 12 = 78 Graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No 4. 0.6, 0.9, 1.2, 1.8, ... ANSWER: SOLUTION: 42, 54, 66, 78 Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No 6. 15, 6, –3, … Find the next four terms of each arithmetic sequence. Then graph the sequence. SOLUTION: Subtract each term from the term directly after it. 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add –9 to the last term. The common difference is 12. Therefore, the sequence is arithmetic. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 To find the next term, add 12 to the last term. –30 + (–9) = –39 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 Graph the sequence. 66 + 12 = 78 Graph the sequence. ANSWER: –12, –21, –30, –39 ANSWER: 42, 54, 66, 78 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. 6. 15, 6, –3, … SOLUTION: The common difference is 8. Subtract each term from the term directly after it. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. –3 + 8 = 5 5 + 8 = 13 The common difference is –9. 13 + 8 = 21 Therefore, the sequence is arithmetic. 21 + 8 = 29 To find the next term, add –9 to the last term. Graph the sequence. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 Graph the sequence. ANSWER: 5, 13, 21, 29 ANSWER: –12, –21, –30, –39 8. –26, –33, –40, … SOLUTION: Subtract each term from the term directly after it. 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. The common difference is –7. Therefore, the sequence is arithmetic. To find the next term, add –7 to the last term. –40 + (–7) = –47 The common difference is 8. –47 + (–7) = –54 Therefore, the sequence is arithmetic. –54 + (–7) = –61 –61 + (–7) = –68 To find the next term, add 8 to the last term. Graph the sequence. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. ANSWER: –47, –54, –61, –68 ANSWER: 5, 13, 21, 29 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. a. How much will Kelly have saved after 8 weeks? 8. –26, –33, –40, … b. If the car costs $2000, how long will it take her to save enough money at this rate? SOLUTION: Subtract each term from the term directly after it. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. The common difference is –7. b. Given an = 2000. Therefore, the sequence is arithmetic. Find n. To find the next term, add –7 to the last term. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 –61 + (–7) = –68 So, it will take about 24 weeks to save $2000. Graph the sequence. ANSWER: a. $850 b. 24 wk Determine whether each sequence is geometric. Write yes or no. 10. –8, –5, –1, 4, … ANSWER: –47, –54, –61, –68 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: 9. FINANCIAL LITERACY Kelly is saving her No money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. 11. 4, 12, 36, 108, … a. How much will Kelly have saved after 8 weeks? b. If the car costs $2000, how long will it take her to SOLUTION: save enough money at this rate? Find the ratio of the consecutive terms. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. Since the ratios are the same, the sequence is geometric. b. Given a = 2000. n ANSWER: Find n. Yes 12. 27, 9, 3, 1, … SOLUTION: So, it will take about 24 weeks to save $2000. Find the ratio of the consecutive terms. ANSWER: a. $850 Since the ratios are the same, the sequence is b. 24 wk geometric. Determine whether each sequence is ANSWER: geometric. Write yes or no. Yes 10. –8, –5, –1, 4, … 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are not the same, the sequence is not geometric. ANSWER: No ANSWER: No 11. 4, 12, 36, 108, … Find the next three terms of each geometric sequence. Then graph the sequence. SOLUTION: Find the ratio of the consecutive terms. 14. 8, 12, 18, 27, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Since the ratios are the same, the sequence is 10-1Y Seesq uences as Functions geometric To find the next term, multiply the previous term by 12. 27, 9, 3, 1, … . SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Graph the sequence. ANSWER: Yes 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: 40.5, 60.75, 91.125 Since the ratios are not the same, the sequence is not geometric. ANSWER: No Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric Since the ratios are the same, the sequence is To find the next term, multiply the previous term by geometric. . eSolutionsManual-PoweredbyCognero To find the next term, multiply the previous termP bayg e5 2. Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 40.5, 60.75, 91.125 16. 250, 50, 10, 2, … SOLUTION: 15. 8, 16, 32, 64, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by Since the ratios are the same, the sequence is geometric. . To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. 17. 9, –3, 1, , … SOLUTION: Since the ratios are the same, the sequence is geometric Find the ratio of the consecutive terms. To find the next term, multiply the previous term by . Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 18. 5, 1, 7, 3, 9, … Since the ratios are the same, the sequence is geometric. SOLUTION: To find the next term, multiply the previous term by . There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Graph the sequence. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. ANSWER: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. The common ratio is . Since the ratios are the same, the sequence is Determine whether each sequence is geometric. arithmetic, geometric, or neither. Explain your reasoning. ANSWER: 18. 5, 1, 7, 3, 9, … Geometric; the common ratio is . SOLUTION: 20. 12, 16, 20, 24, … SOLUTION: There is no common difference. To find the common difference, subtract any term Therefore, the sequence is not arithmetic. from the term directly after it. Find the ratio of the consecutive terms. The common difference is 4. Since the ratios are not the same, the sequence is not Therefore, the sequence is arithmetic. geometric. Find the ratio of the consecutive terms. ANSWER: Neither; there is no common difference or ratio. Since the ratios are not the same, the sequence is not 19. 200, –100, 50, –25, … geometric. SOLUTION: ANSWER: To find the common difference, subtract any term Arithmetic; the common difference is 4. from the term directly after it. Determine whether each sequence is arithmetic. Write yes or no. There is no common difference. 21. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. SOLUTION: Subtract any term from the term directly after it. The common ratio is . Since the ratios are the same, the sequence is geometric. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: ANSWER: Geometric; the common ratio is . No 20. 12, 16, 20, 24, … 22. –9, –3, 0, 3, 9 SOLUTION: SOLUTION: To find the common difference, subtract any term Subtract any term from the term directly after it. from the term directly after it. There is no common difference. The common difference is 4. Therefore, the sequence is not arithmetic. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. ANSWER: No 23. 14, –5, –19, … Since the ratios are not the same, the sequence is not geometric. SOLUTION: Subtract any term from the term directly after it. ANSWER: Arithmetic; the common difference is 4. Determine whether each sequence is There is no common difference. arithmetic. Write yes or no. Therefore, the sequence is not arithmetic. 21. ANSWER: No SOLUTION: Subtract any term from the term directly after it. 24. SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No The common difference is . Therefore, the sequence is arithmetic. 22. –9, –3, 0, 3, 9 ANSWER: SOLUTION: Yes Subtract any term from the term directly after it. Find the next four terms of each arithmetic sequence. Then graph the sequence. There is no common difference. 25. –4, –1, 2, 5,… Therefore, the sequence is not arithmetic. SOLUTION: Subtract any term from the term directly after it. ANSWER: No 23. 14, –5, –19, … The common difference is 3. Therefore, the sequence is arithmetic. SOLUTION: Subtract any term from the term directly after it. To find the next term, add 3 to the last term. 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 There is no common difference. 14 + 3 = 17 Therefore, the sequence is not arithmetic. Graph the sequence. ANSWER: No 24. SOLUTION: Subtract any term from the term directly after it. ANSWER: 8, 11, 14, 17 The common difference is . Therefore, the sequence is arithmetic. ANSWER: Yes Find the next four terms of each arithmetic 26. 10, 2, –6, –14, … sequence. Then graph the sequence. 25. –4, –1, 2, 5,… SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. The common difference is 3. To find the next term, add –8 to the last term. Therefore, the sequence is arithmetic. –14 + (–8) = –22 To find the next term, add 3 to the last term. –22 + (–8) = –30 –30 + (–8) = –38 5 + 3 = 8 –38 + (–8) = –46 8 + 3 = 11 11 + 3 = 14 Graph the sequence. 14 + 3 = 17 Graph the sequence. ANSWER: –22, –30, –38, – 46 ANSWER: 8, 11, 14, 17 27. –5, –11, –17, –23, … SOLUTION: 26. 10, 2, –6, –14, … Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. The common difference is –8. Therefore, this sequence is arithmetic. –23 + (–6) = –29 –29 + (–6) = –35 To find the next term, add –8 to the last term. –35 + (–6) = –41 –41 + (–6) = –47 –14 + (–8) = –22 –22 + (–8) = –30 Graph the sequence. –30 + (–8) = –38 –38 + (–8) = –46 Graph the sequence. ANSWER: –29, –35, – 41, – 47 ANSWER: –22, –30, –38, – 46 28. –19, –2, 15, … 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. To find the next term, add –6 to the last term. 15 + 17 = 32 32 + 17 = 49 –23 + (–6) = –29 49 + 17 = 66 –29 + (–6) = –35 66 + 17 = 83 –35 + (–6) = –41 –41 + (–6) = –47 Graph the sequence. Graph the sequence. ANSWER: 32, 49, 66, 83 ANSWER: –29, –35, – 41, – 47 29. 28. –19, –2, 15, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. The common difference is . Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 To find the next term, add to the last term. 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 Graph the sequence. Graph the sequence. ANSWER: 32, 49, 66, 83 ANSWER: 29. SOLUTION: Subtract any term from the term directly after it. 30. SOLUTION: The common difference is . Subtract any term from the term directly after it. Therefore, the sequence is arithmetic. To find the next term, add to the last term. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 30. SOLUTION: Subtract any term from the term directly after it. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: The common difference is –1. Therefore, the sequence is arithmetic. Given a = 28, d = 2 and n = 24. 1 To find the next term, add −1 to the last term. Find a . 24 ANSWER: 74 Graph the sequence. 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue indefinitely? Explain. ANSWER: SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Find a . 18 Therefore he will row for 30 minutes and 30 seconds on the 38th day. b. Given a = 5, d = 1.5 and a = 60. 31. THEATER There are 28 seats in the front row of a 1 n theater. Each successive row contains two more Find n. seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: Given a = 28, d = 2 and n = 24. 1 Mario will first row an hour or more on the 38th day. Find a . 24 c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing. ANSWER: a. 30 minutes and 30 seconds ANSWER: b. on the 38th day 74 c. Sample answer: It is unreasonable because there 32. CCSS SENSE-MAKING Mario began an exercise are only so many hours in the day that can be program to get back in shape. He plans to row 5 dedicated to rowing. minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. Determine whether each sequence is geometric. Write yes or no. a. How long will he row on the 18th day? 33. 21, 14, 7, … b. On what day will Mario first row an hour or more? SOLUTION: c. Is it reasonable for this pattern to continue Find the ratio of the consecutive terms. indefinitely? Explain. SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Since the ratios are not the same, the sequence is not geometric. Find a . 18 ANSWER: No Therefore he will row for 30 minutes and 30 seconds 34. 124, 186, 248, … on the 38th day. b. Given a = 5, d = 1.5 and a = 60. SOLUTION: 1 n Find n. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Mario will first row an hour or more on the 38th day. ANSWER: c. Sample answer: It is unreasonable because there are only so many hours in the day that can be No dedicated to rowing. 35. –27, 18, –12, … ANSWER: SOLUTION: a. 30 minutes and 30 seconds Find the ratio of the consecutive terms. b. on the 38th day Since the ratios are the same, the sequence is c. Sample answer: It is unreasonable because there geometric. are only so many hours in the day that can be dedicated to rowing. ANSWER: Yes Determine whether each sequence is 36. 162, 108, 72, … geometric. Write yes or no. SOLUTION: 33. 21, 14, 7, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. ANSWER: Since the ratios are not the same, the sequence is not Yes geometric. 37. ANSWER: No SOLUTION: Find the ratio of the consecutive terms. 34. 124, 186, 248, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Since the ratios are not same, the sequence is not ANSWER: geometric. No ANSWER: 35. –27, 18, –12, … No SOLUTION: Find the ratio of the consecutive terms. 38. –4, –2, 0, 2, … Since the ratios are the same, the sequence is SOLUTION: geometric. Find the ratio of the consecutive terms. ANSWER: Yes 36. 162, 108, 72, … Since the ratios are not same, the sequence is not geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: No Find the next three terms of the sequence. Since the ratios are same, the sequence is geometric. Then graph the sequence. 39. 0.125, –0.5, 2, … ANSWER: Yes SOLUTION: Find the ratio of the consecutive terms. 37. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: No 38. –4, –2, 0, 2, … ANSWER: SOLUTION: – 8, 32, –128 Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: No Find the next three terms of the sequence. 40. 18, 12, 8, … Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric . To find the next term, multiply the previous term with −4. Graph the sequence. Graph the sequence. ANSWER: – 8, 32, –128 ANSWER: 40. 18, 12, 8, … SOLUTION: 41. 64, 48, 36, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric. . To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 41. 64, 48, 36, … 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric . To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 42. 81, 108, 144, … SOLUTION: 43. Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 27, 81, 243 44. 1, 0.1, 0.01, 0.001, … 43. SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 0.1. To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: 0.0001, 0.00001, 0.000001 ANSWER: 27, 81, 243 Determine whether each sequence is arithmetic, geometric, or neither. Explain your 44. 1, 0.1, 0.01, 0.001, … reasoning. 45. 3, 12, 27, 48, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by There is no common difference. 0.1. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … ANSWER: SOLUTION: 0.0001, 0.00001, 0.000001 Subtract each term from the term directly after it. The common difference is –3. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. Determine whether each sequence is arithmetic, geometric, or neither. Explain your Since the ratios are not same, the sequence is not reasoning. geometric. 45. 3, 12, 27, 48, … ANSWER: Arithmetic; the common difference is –3. SOLUTION: Subtract each term from the term directly after it. 47. 12, 36, 108, 324, … SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the There is no common difference. consecutive terms. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: The common ratio is 3. Neither; there is no common difference or ratio. Since the ratios are same, the sequence is geometric. 46. 1, –2, –5, –8, … ANSWER: Geometric; the common ratio is 3. SOLUTION: Subtract each term from the term directly after it. 48. The common difference is –3. SOLUTION: Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, this sequence is not arithmetic. Since the ratios are not same, the sequence is not geometric. To find the common ratio, find the ratio of the consecutive terms. ANSWER: Arithmetic; the common difference is –3. 47. 12, 36, 108, 324, … The common ratio is . SOLUTION: Subtract each term from the term directly after it. Since the ratios are the same, the sequence is geometric. ANSWER: There is no common difference. Geometric; the common ratio is . Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. 49. SOLUTION: Subtract each term from the term directly after it. The common ratio is 3. Since the ratios are same, the sequence is geometric. ANSWER: Geometric; the common ratio is 3. The common difference is . Therefore, the sequence is arithmetic. 48. To find the common ratio, find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not geometric. There is no common difference. ANSWER: Therefore, this sequence is not arithmetic. Arithmetic; the common difference is . To find the common ratio, find the ratio of the consecutive terms. 50. 6, 9, 14, 21, … SOLUTION: Subtract each term from the term directly after it. The common ratio is . Since the ratios are the same, the sequence is geometric. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: To find the common ratio, find the ratio of the Geometric; the common ratio is . consecutive terms. 49. Since the ratios are not same, the sequence is not geometric. SOLUTION: Subtract each term from the term directly after it. ANSWER: Neither; there is no common difference or ratio. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day The common difference is . to finish the book by the end of her vacation? Therefore, the sequence is arithmetic. SOLUTION: To find the common ratio, find the ratio of the consecutive terms. The number of pages to be read is 800 – 112 or 688. The minimum number of pages to read per day is . Since the ratios are not same, the sequence is not geometric. ANSWER: 86 pg/day ANSWER: Arithmetic; the common difference is . 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? 50. 6, 9, 14, 21, … SOLUTION: SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in Subtract each term from the term directly after it. then evaluate. There is no common difference. Therefore, the sequence is not arithmetic. The worth of the car will be about $9052 after 6 years. To find the common ratio, find the ratio of the consecutive terms. ANSWER: $9052 Since the ratios are not same, the sequence is not 53. CCSS REGULARITY When a piece of paper is geometric. folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, how thick would it be? ANSWER: Neither; there is no common difference or ratio. SOLUTION: Given a = 0.1, n = 37 and r = 2. 0 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is Find a . 37 going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation? SOLUTION: The number of pages to be read is 800 – 112 or 688. The thickness would be about 13,744 km. The minimum number of pages to read per day is . ANSWER: about 13,744 km ANSWER: 54. REASONING Explain why the sequence 8, 10, 13, 86 pg/day 17, 22 is not arithmetic. SOLUTION: 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is Sample answer: The consecutive terms do not share currently valued at $24,000, to the nearest dollar, a common difference. For instance, 22 – 17 = 5, how much will it be worth in 6 years? while 17 – 13 = 4. SOLUTION: ANSWER: Substitute 0.15, 6 and 24000 for r, t and P in Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, then evaluate. while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. The worth of the car will be about $9052 after 6 years. SOLUTION: Sample answer: A babysitter earns $20 for cleaning ANSWER: the house and $8 extra for every hour she watches $9052 the children. 53. CCSS REGULARITY When a piece of paper is ANSWER: folded onto itself, it doubles in thickness. If a piece of Sample answer: A babysitter earns $20 for cleaning paper that is 0.1 mm thick could be folded 37 times, the house and $8 extra for every hour she watches how thick would it be? the children. SOLUTION: 56. CHALLENGE The sum of three consecutive terms Given a0 = 0.1, n = 37 and r = 2. of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. Find a . 37 SOLUTION: Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. The thickness would be about 13,744 km. ANSWER: about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. Sample answer: Let d = 5. SOLUTION: Therefore, the terms are –3, 2, 7. Sample answer: The consecutive terms do not share ANSWER: a common difference. For instance, 22 – 17 = 5, –3, 2, 7 while 17 – 13 = 4. 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is ANSWER: arithmetic, geometric, neither, or both. Is either of Sample answer: The consecutive terms do not share them correct? Explain your reasoning. a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. ANSWER: SOLUTION: Sample answer: Neither; the sequence is both Let x be the first term in the arithmetic sequence. arithmetic and geometric. Therefore, the next two terms should be x + d and x + 2d. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: –3, 2, 7 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Yes 3. 1, 2, 4, 8, 16 SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: Determine whether each sequence is arithmetic No no. 1. 8, –2, –12, –22 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: Yes ANSWER: No 2. –19, –12, –5, 2, 9 Find the next four terms of each arithmetic sequence. Then graph the sequence. SOLUTION: Subtract each term from the term directly after it. 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: The common difference is 12. Therefore, the sequence is arithmetic. Yes To find the next term, add 12 to the last term. 3. 1, 2, 4, 8, 16 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 SOLUTION: 66 + 12 = 78 Subtract each term from the term directly after it. Graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No 4. 0.6, 0.9, 1.2, 1.8, ... ANSWER: 42, 54, 66, 78 SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No 6. 15, 6, –3, … Find the next four terms of each arithmetic SOLUTION: sequence. Then graph the sequence. Subtract each term from the term directly after it. 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add –9 to the last term. The common difference is 12. –3 + (–9) = –12 Therefore, the sequence is arithmetic. –12 + (–9) = –21 –21 + (–9) = –30 To find the next term, add 12 to the last term. –30 + (–9) = –39 30 + 12 = 42 42 + 12 = 54 Graph the sequence. 54 + 12 = 66 66 + 12 = 78 Graph the sequence. ANSWER: –12, –21, –30, –39 ANSWER: 42, 54, 66, 78 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. 6. 15, 6, –3, … The common difference is 8. SOLUTION: Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the next term, add 8 to the last term. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 The common difference is –9. 21 + 8 = 29 Therefore, the sequence is arithmetic. Graph the sequence. To find the next term, add –9 to the last term. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 Graph the sequence. ANSWER: 5, 13, 21, 29 ANSWER: –12, –21, –30, –39 8. –26, –33, –40, … SOLUTION: Subtract each term from the term directly after it. 7. –19, –11, –3, … SOLUTION: The common difference is –7. Subtract each term from the term directly after it. Therefore, the sequence is arithmetic. To find the next term, add –7 to the last term. –40 + (–7) = –47 –47 + (–7) = –54 The common difference is 8. –54 + (–7) = –61 Therefore, the sequence is arithmetic. –61 + (–7) = –68 To find the next term, add 8 to the last term. Graph the sequence. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. ANSWER: –47, –54, –61, –68 ANSWER: 5, 13, 21, 29 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. a. How much will Kelly have saved after 8 weeks? 8. –26, –33, –40, … b. If the car costs $2000, how long will it take her to save enough money at this rate? SOLUTION: Subtract each term from the term directly after it. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. b. Given a = 2000. n The common difference is –7. Therefore, the sequence is arithmetic. Find n. To find the next term, add –7 to the last term. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 –61 + (–7) = –68 So, it will take about 24 weeks to save $2000. Graph the sequence. ANSWER: a. $850 b. 24 wk Determine whether each sequence is geometric. Write yes or no. 10. –8, –5, –1, 4, … ANSWER: –47, –54, –61, –68 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: No 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. 11. 4, 12, 36, 108, … a. How much will Kelly have saved after 8 weeks? SOLUTION: b. If the car costs $2000, how long will it take her to Find the ratio of the consecutive terms. save enough money at this rate? SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 Since the ratios are the same, the sequence is After 8 weeks, she will have 250 + (8 × 75) or $850. geometric. b. Given a = 2000. n ANSWER: Find n. Yes 12. 27, 9, 3, 1, … SOLUTION: Find the ratio of the consecutive terms. So, it will take about 24 weeks to save $2000. ANSWER: a. $850 Since the ratios are the same, the sequence is geometric. b. 24 wk ANSWER: Determine whether each sequence is geometric. Write yes or no. Yes 10. –8, –5, –1, 4, … 13. 7, 14, 21, 28, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not Since the ratios are not the same, the sequence is not geometric. geometric. ANSWER: ANSWER: No No 11. 4, 12, 36, 108, … Find the next three terms of each geometric sequence. Then graph the sequence. SOLUTION: 14. 8, 12, 18, 27, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are the same, the sequence is ANSWER: geometric Yes To find the next term, multiply the previous term by 12. 27, 9, 3, 1, … . SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Graph the sequence. ANSWER: Yes 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: 40.5, 60.75, 91.125 Since the ratios are not the same, the sequence is not geometric. ANSWER: No Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 40.5, 60.75, 91.125 16. 250, 50, 10, 2, … 10-1 Sequences as Functions SOLUTION: 15. 8, 16, 32, 64, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by Since the ratios are the same, the sequence is . geometric. To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. eSolutionsManual-PoweredbyCognero 17. 9, –3, 1, , … Page6 SOLUTION: Since the ratios are the same, the sequence is Find the ratio of the consecutive terms. geometric To find the next term, multiply the previous term by . Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 17. 9, –3, 1, , … SOLUTION: Determine whether each sequence is Find the ratio of the consecutive terms. arithmetic, geometric, or neither. Explain your reasoning. 18. 5, 1, 7, 3, 9, … Since the ratios are the same, the sequence is SOLUTION: geometric. To find the next term, multiply the previous term by . There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Graph the sequence. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. ANSWER: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. The common ratio is . Since the ratios are the same, the sequence is geometric. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. ANSWER: 18. 5, 1, 7, 3, 9, … Geometric; the common ratio is . SOLUTION: 20. 12, 16, 20, 24, … SOLUTION: To find the common difference, subtract any term There is no common difference. from the term directly after it. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. The common difference is 4. Therefore, the sequence is arithmetic. Since the ratios are not the same, the sequence is not geometric. Find the ratio of the consecutive terms. ANSWER: Neither; there is no common difference or ratio. Since the ratios are not the same, the sequence is not geometric. 19. 200, –100, 50, –25, … ANSWER: SOLUTION: Arithmetic; the common difference is 4. To find the common difference, subtract any term from the term directly after it. Determine whether each sequence is arithmetic. Write yes or no. 21. There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. SOLUTION: Subtract any term from the term directly after it. The common ratio is . Since the ratios are the same, the sequence is There is no common difference. geometric. Therefore, the sequence is not arithmetic. ANSWER: ANSWER: Geometric; the common ratio is . No 20. 12, 16, 20, 24, … 22. –9, –3, 0, 3, 9 SOLUTION: SOLUTION: To find the common difference, subtract any term Subtract any term from the term directly after it. from the term directly after it. There is no common difference. The common difference is 4. Therefore, the sequence is not arithmetic. Therefore, the sequence is arithmetic. ANSWER: Find the ratio of the consecutive terms. No 23. 14, –5, –19, … Since the ratios are not the same, the sequence is not geometric. SOLUTION: Subtract any term from the term directly after it. ANSWER: Arithmetic; the common difference is 4. Determine whether each sequence is There is no common difference. arithmetic. Write yes or no. Therefore, the sequence is not arithmetic. 21. ANSWER: No SOLUTION: Subtract any term from the term directly after it. 24. SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No The common difference is . Therefore, the sequence is arithmetic. 22. –9, –3, 0, 3, 9 ANSWER: Yes SOLUTION: Subtract any term from the term directly after it. Find the next four terms of each arithmetic sequence. Then graph the sequence. 25. –4, –1, 2, 5,… There is no common difference. Therefore, the sequence is not arithmetic. SOLUTION: Subtract any term from the term directly after it. ANSWER: No 23. 14, –5, –19, … The common difference is 3. Therefore, the sequence is arithmetic. SOLUTION: To find the next term, add 3 to the last term. Subtract any term from the term directly after it. 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 14 + 3 = 17 There is no common difference. Therefore, the sequence is not arithmetic. Graph the sequence. ANSWER: No 24. SOLUTION: Subtract any term from the term directly after it. ANSWER: 8, 11, 14, 17 The common difference is . Therefore, the sequence is arithmetic. ANSWER: Yes 26. 10, 2, –6, –14, … Find the next four terms of each arithmetic sequence. Then graph the sequence. SOLUTION: 25. –4, –1, 2, 5,… Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. The common difference is 3. Therefore, the sequence is arithmetic. –14 + (–8) = –22 –22 + (–8) = –30 To find the next term, add 3 to the last term. –30 + (–8) = –38 –38 + (–8) = –46 5 + 3 = 8 8 + 3 = 11 Graph the sequence. 11 + 3 = 14 14 + 3 = 17 Graph the sequence. ANSWER: –22, –30, –38, – 46 ANSWER: 8, 11, 14, 17 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. 26. 10, 2, –6, –14, … SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. The common difference is –8. Therefore, this sequence is arithmetic. –23 + (–6) = –29 –29 + (–6) = –35 To find the next term, add –8 to the last term. –35 + (–6) = –41 –41 + (–6) = –47 –14 + (–8) = –22 –22 + (–8) = –30 Graph the sequence. –30 + (–8) = –38 –38 + (–8) = –46 Graph the sequence. ANSWER: –29, –35, – 41, – 47 ANSWER: –22, –30, –38, – 46 28. –19, –2, 15, … 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. The common difference is –6. To find the next term, add 17 to the last term. Therefore, the sequence is arithmetic. 15 + 17 = 32 To find the next term, add –6 to the last term. 32 + 17 = 49 49 + 17 = 66 –23 + (–6) = –29 66 + 17 = 83 –29 + (–6) = –35 –35 + (–6) = –41 Graph the sequence. –41 + (–6) = –47 Graph the sequence. ANSWER: 32, 49, 66, 83 ANSWER: –29, –35, – 41, – 47 29. 28. –19, –2, 15, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. The common difference is . Therefore, the sequence is arithmetic. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. To find the next term, add to the last term. 15 + 17 = 32 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 Graph the sequence. Graph the sequence. ANSWER: 32, 49, 66, 83 ANSWER: 29. SOLUTION: Subtract any term from the term directly after it. 30. SOLUTION: The common difference is . Subtract any term from the term directly after it. Therefore, the sequence is arithmetic. To find the next term, add to the last term. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 30. SOLUTION: Subtract any term from the term directly after it. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: The common difference is –1. Given a = 28, d = 2 and n = 24. 1 Therefore, the sequence is arithmetic. Find a . To find the next term, add −1 to the last term. 24 ANSWER: 74 32. CCSS SENSE-MAKING Mario began an exercise Graph the sequence. program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue indefinitely? Explain. ANSWER: SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Find a . 18 Therefore he will row for 30 minutes and 30 seconds on the 38th day. b. Given a = 5, d = 1.5 and a = 60. 1 n 31. THEATER There are 28 seats in the front row of a Find n. theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: Given a1 = 28, d = 2 and n = 24. Mario will first row an hour or more on the 38th day. Find a . c. Sample answer: It is unreasonable because there 24 are only so many hours in the day that can be dedicated to rowing. ANSWER: a. 30 minutes and 30 seconds ANSWER: b. on the 38th day 74 c. Sample answer: It is unreasonable because there are only so many hours in the day that can be 32. CCSS SENSE-MAKING Mario began an exercise dedicated to rowing. program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty Determine whether each sequence is seconds each day. geometric. Write yes or no. a. How long will he row on the 18th day? 33. 21, 14, 7, … b. On what day will Mario first row an hour or more? SOLUTION: Find the ratio of the consecutive terms. c. Is it reasonable for this pattern to continue indefinitely? Explain. SOLUTION: a. Given a = 5, d = 1.5 and n = 18. Since the ratios are not the same, the sequence is not 1 geometric. Find a . 18 ANSWER: No 34. 124, 186, 248, … Therefore he will row for 30 minutes and 30 seconds on the 38th day. SOLUTION: b. Given a = 5, d = 1.5 and a = 60. 1 n Find the ratio of the consecutive terms. Find n. Since the ratios are not the same, the sequence is not geometric. Mario will first row an hour or more on the 38th day. ANSWER: c. Sample answer: It is unreasonable because there No are only so many hours in the day that can be dedicated to rowing. 35. –27, 18, –12, … SOLUTION: ANSWER: Find the ratio of the consecutive terms. a. 30 minutes and 30 seconds b. on the 38th day Since the ratios are the same, the sequence is geometric. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be ANSWER: dedicated to rowing. Yes 36. 162, 108, 72, … Determine whether each sequence is geometric. Write yes or no. SOLUTION: 33. 21, 14, 7, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. ANSWER: Yes Since the ratios are not the same, the sequence is not geometric. 37. ANSWER: No SOLUTION: Find the ratio of the consecutive terms. 34. 124, 186, 248, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Since the ratios are not same, the sequence is not ANSWER: geometric. No ANSWER: 35. –27, 18, –12, … No SOLUTION: Find the ratio of the consecutive terms. 38. –4, –2, 0, 2, … SOLUTION: Since the ratios are the same, the sequence is geometric. Find the ratio of the consecutive terms. ANSWER: Yes 36. 162, 108, 72, … Since the ratios are not same, the sequence is not geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. Since the ratios are same, the sequence is geometric. 39. 0.125, –0.5, 2, … ANSWER: Yes SOLUTION: Find the ratio of the consecutive terms. 37. SOLUTION: Since the ratios are same, the sequence is geometric Find the ratio of the consecutive terms. To find the next term, multiply the previous term with −4. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: No 38. –4, –2, 0, 2, … ANSWER: SOLUTION: – 8, 32, –128 Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: No Find the next three terms of the sequence. 40. 18, 12, 8, … Then graph the sequence. SOLUTION: 39. 0.125, –0.5, 2, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric . To find the next term, multiply the previous term with −4. Graph the sequence. Graph the sequence. ANSWER: – 8, 32, –128 ANSWER: 40. 18, 12, 8, … SOLUTION: 41. 64, 48, 36, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric. . To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 41. 64, 48, 36, … 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by To find the next term, multiply the previous term by . . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 42. 81, 108, 144, … 43. SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric . To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 27, 81, 243 44. 1, 0.1, 0.01, 0.001, … 43. SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric 0.1. To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: 0.0001, 0.00001, 0.000001 ANSWER: 27, 81, 243 Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 44. 1, 0.1, 0.01, 0.001, … 45. 3, 12, 27, 48, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are same, the sequence is geometric. There is no common difference. To find the next term, multiply the previous term by 0.1. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … SOLUTION: ANSWER: Subtract each term from the term directly after it. 0.0001, 0.00001, 0.000001 The common difference is –3. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. Determine whether each sequence is Since the ratios are not same, the sequence is not arithmetic, geometric, or neither. Explain your geometric. reasoning. 45. 3, 12, 27, 48, … ANSWER: Arithmetic; the common difference is –3. SOLUTION: Subtract each term from the term directly after it. 47. 12, 36, 108, 324, … SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. There is no common difference. To find the common ratio, find the ratio of the consecutive terms. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. The common ratio is 3. ANSWER: Neither; there is no common difference or ratio. Since the ratios are same, the sequence is geometric. ANSWER: 46. 1, –2, –5, –8, … Geometric; the common ratio is 3. SOLUTION: Subtract each term from the term directly after it. 48. SOLUTION: The common difference is –3. Subtract each term from the term directly after it. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, this sequence is not arithmetic. Since the ratios are not same, the sequence is not To find the common ratio, find the ratio of the geometric. consecutive terms. ANSWER: Arithmetic; the common difference is –3. 47. 12, 36, 108, 324, … The common ratio is . SOLUTION: Since the ratios are the same, the sequence is Subtract each term from the term directly after it. geometric. ANSWER: Geometric; the common ratio is . There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the 49. consecutive terms. SOLUTION: Subtract each term from the term directly after it. The common ratio is 3. Since the ratios are same, the sequence is geometric. ANSWER: Geometric; the common ratio is 3. The common difference is . Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the 48. consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not geometric. ANSWER: There is no common difference. Therefore, this sequence is not arithmetic. Arithmetic; the common difference is . To find the common ratio, find the ratio of the consecutive terms. 50. 6, 9, 14, 21, … SOLUTION: Subtract each term from the term directly after it. The common ratio is . Since the ratios are the same, the sequence is geometric. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: To find the common ratio, find the ratio of the consecutive terms. Geometric; the common ratio is . 49. Since the ratios are not same, the sequence is not geometric. SOLUTION: Subtract each term from the term directly after it. ANSWER: Neither; there is no common difference or ratio. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation? The common difference is . Therefore, the sequence is arithmetic. SOLUTION: To find the common ratio, find the ratio of the The number of pages to be read is 800 – 112 or 688. consecutive terms. The minimum number of pages to read per day is . Since the ratios are not same, the sequence is not geometric. ANSWER: 86 pg/day ANSWER: 52. DEPRECIATION Tammy’s car is expected to Arithmetic; the common difference is . depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? 50. 6, 9, 14, 21, … SOLUTION: SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in Subtract each term from the term directly after it. then evaluate. There is no common difference. The worth of the car will be about $9052 after 6 Therefore, the sequence is not arithmetic. years. To find the common ratio, find the ratio of the consecutive terms. ANSWER: $9052 53. CCSS REGULARITY When a piece of paper is Since the ratios are not same, the sequence is not folded onto itself, it doubles in thickness. If a piece of geometric. paper that is 0.1 mm thick could be folded 37 times, how thick would it be? ANSWER: SOLUTION: Neither; there is no common difference or ratio. Given a = 0.1, n = 37 and r = 2. 0 51. READING Sareeta took an 800-page book on Find a . vacation. If she was already on page 112 and is 37 going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation? SOLUTION: The number of pages to be read is 800 – 112 or 688. The thickness would be about 13,744 km. The minimum number of pages to read per day is ANSWER: . about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, ANSWER: 17, 22 is not arithmetic. 86 pg/day SOLUTION: 52. DEPRECIATION Tammy’s car is expected to Sample answer: The consecutive terms do not share depreciate at a rate of 15% per year. If her car is a common difference. For instance, 22 – 17 = 5, currently valued at $24,000, to the nearest dollar, while 17 – 13 = 4. how much will it be worth in 6 years? ANSWER: SOLUTION: Sample answer: The consecutive terms do not share Substitute 0.15, 6 and 24000 for r, t and P in a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. then evaluate. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. The worth of the car will be about $9052 after 6 years. SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches ANSWER: the children. $9052 ANSWER: 53. CCSS REGULARITY When a piece of paper is Sample answer: A babysitter earns $20 for cleaning folded onto itself, it doubles in thickness. If a piece of the house and $8 extra for every hour she watches paper that is 0.1 mm thick could be folded 37 times, the children. how thick would it be? 56. CHALLENGE The sum of three consecutive terms SOLUTION: of an arithmetic sequence is 6. The product of the Given a = 0.1, n = 37 and r = 2. 0 terms is –42. Find the terms. SOLUTION: Find a . 37 Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. The thickness would be about 13,744 km. ANSWER: about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. SOLUTION: ANSWER: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, –3, 2, 7 while 17 – 13 = 4. 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of ANSWER: them correct? Explain your reasoning. Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches SOLUTION: the children. Sample answer: Neither; the sequence is both arithmetic and geometric. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. ANSWER: Sample answer: Neither; the sequence is both SOLUTION: arithmetic and geometric. Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: –3, 2, 7 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Yes 3. 1, 2, 4, 8, 16 SOLUTION: Subtract each term from the term directly after it. Determine whether each sequence is arithmetic no. There is no common difference. Therefore, the sequence is not arithmetic. 1. 8, –2, –12, –22 SOLUTION: ANSWER: Subtract each term from the term directly after it. No 4. 0.6, 0.9, 1.2, 1.8, ... The common difference is –10. Therefore, the sequence is arithmetic. SOLUTION: Subtract each term from the term directly after it. ANSWER: Yes There is no common difference. 2. –19, –12, –5, 2, 9 Therefore, the sequence is not arithmetic. SOLUTION: ANSWER: Subtract each term from the term directly after it. No Find the next four terms of each arithmetic sequence. Then graph the sequence. The common difference is 7. Therefore, the sequence is arithmetic. 5. 6, 18, 30, … SOLUTION: ANSWER: Subtract each term from the term directly after it. Yes 3. 1, 2, 4, 8, 16 The common difference is 12. SOLUTION: Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the next term, add 12 to the last term. 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 There is no common difference. 66 + 12 = 78 Therefore, the sequence is not arithmetic. Graph the sequence. ANSWER: No 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: Subtract each term from the term directly after it. ANSWER: 42, 54, 66, 78 There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No Find the next four terms of each arithmetic sequence. Then graph the sequence. 5. 6, 18, 30, … 6. 15, 6, –3, … SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is 12. Therefore, the sequence is arithmetic. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. 30 + 12 = 42 To find the next term, add –9 to the last term. 42 + 12 = 54 54 + 12 = 66 –3 + (–9) = –12 66 + 12 = 78 –12 + (–9) = –21 –21 + (–9) = –30 Graph the sequence. –30 + (–9) = –39 Graph the sequence. ANSWER: 42, 54, 66, 78 ANSWER: –12, –21, –30, –39 7. –19, –11, –3, … 6. 15, 6, –3, … SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is 8. The common difference is –9. Therefore, the sequence is arithmetic. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. To find the next term, add –9 to the last term. –3 + 8 = 5 –3 + (–9) = –12 5 + 8 = 13 –12 + (–9) = –21 13 + 8 = 21 –21 + (–9) = –30 21 + 8 = 29 –30 + (–9) = –39 Graph the sequence. Graph the sequence. ANSWER: ANSWER: 5, 13, 21, 29 –12, –21, –30, –39 7. –19, –11, –3, … 8. –26, –33, –40, … SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is 8. The common difference is –7. Therefore, the sequence is arithmetic. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. To find the next term, add –7 to the last term. –3 + 8 = 5 –40 + (–7) = –47 5 + 8 = 13 –47 + (–7) = –54 13 + 8 = 21 –54 + (–7) = –61 21 + 8 = 29 –61 + (–7) = –68 Graph the sequence. Graph the sequence. ANSWER: ANSWER: 5, 13, 21, 29 –47, –54, –61, –68 8. –26, –33, –40, … 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. SOLUTION: Subtract each term from the term directly after it. a. How much will Kelly have saved after 8 weeks? b. If the car costs $2000, how long will it take her to save enough money at this rate? The common difference is –7. SOLUTION: Therefore, the sequence is arithmetic. a. Given a = 250, d = 75 and n = 8. 0 To find the next term, add –7 to the last term. After 8 weeks, she will have 250 + (8 × 75) or $850. –40 + (–7) = –47 b. Given a = 2000. –47 + (–7) = –54 n –54 + (–7) = –61 –61 + (–7) = –68 Find n. Graph the sequence. So, it will take about 24 weeks to save $2000. ANSWER: a. $850 b. 24 wk ANSWER: –47, –54, –61, –68 Determine whether each sequence is geometric. Write yes or no. 10. –8, –5, –1, 4, … SOLUTION: Find the ratio of the consecutive terms. 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to Since the ratios are not same, the sequence is not save $75 per week from her job as a waitress. geometric. a. How much will Kelly have saved after 8 weeks? ANSWER: No b. If the car costs $2000, how long will it take her to save enough money at this rate? 11. 4, 12, 36, 108, … SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 SOLUTION: After 8 weeks, she will have 250 + (8 × 75) or $850. Find the ratio of the consecutive terms. b. Given an = 2000. Find n. Since the ratios are the same, the sequence is geometric. ANSWER: Yes So, it will take about 24 weeks to save $2000. 12. 27, 9, 3, 1, … ANSWER: a. $850 SOLUTION: Find the ratio of the consecutive terms. b. 24 wk Determine whether each sequence is geometric. Write yes or no. Since the ratios are the same, the sequence is 10. –8, –5, –1, 4, … geometric. SOLUTION: ANSWER: Find the ratio of the consecutive terms. Yes 13. 7, 14, 21, 28, … Since the ratios are not same, the sequence is not SOLUTION: geometric. Find the ratio of the consecutive terms. ANSWER: No Since the ratios are not the same, the sequence is not geometric. 11. 4, 12, 36, 108, … ANSWER: SOLUTION: No Find the ratio of the consecutive terms. Find the next three terms of each geometric sequence. Then graph the sequence. Since the ratios are the same, the sequence is 14. 8, 12, 18, 27, … geometric. SOLUTION: ANSWER: Find the ratio of the consecutive terms. Yes 12. 27, 9, 3, 1, … Since the ratios are the same, the sequence is SOLUTION: geometric Find the ratio of the consecutive terms. To find the next term, multiply the previous term by . Since the ratios are the same, the sequence is geometric. ANSWER: Yes Graph the sequence. 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. ANSWER: ANSWER: No 40.5, 60.75, 91.125 Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … SOLUTION: Find the ratio of the consecutive terms. 15. 8, 16, 32, 64, … Since the ratios are the same, the sequence is geometric SOLUTION: Find the ratio of the consecutive terms. To find the next term, multiply the previous term by . Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: 40.5, 60.75, 91.125 ANSWER: 128, 256, 512 15. 8, 16, 32, 64, … SOLUTION: 16. 250, 50, 10, 2, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are the same, the sequence is To find the next term, multiply the previous term by geometric 2. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric 17. 9, –3, 1, , … To find the next term, multiply the previous term by . SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Graph the sequence. To find the next term, multiply the previous term by . Graph the sequence. ANSWER: ANSWER: 10-1 Sequences as Functions 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is Determine whether each sequence is geometric. arithmetic, geometric, or neither. Explain your reasoning. To find the next term, multiply the previous term by 18. 5, 1, 7, 3, 9, … . SOLUTION: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not the same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … ANSWER: SOLUTION: To find the common difference, subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. eSolutionsManual-PoweredbyCognero Page7 Find the ratio of the consecutive terms. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. The common ratio is . 18. 5, 1, 7, 3, 9, … Since the ratios are the same, the sequence is geometric. SOLUTION: ANSWER: Geometric; the common ratio is . There is no common difference. Therefore, the sequence is not arithmetic. 20. 12, 16, 20, 24, … Find the ratio of the consecutive terms. SOLUTION: To find the common difference, subtract any term from the term directly after it. Since the ratios are not the same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. The common difference is 4. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. Since the ratios are not the same, the sequence is not geometric. ANSWER: Arithmetic; the common difference is 4. There is no common difference. Therefore, the sequence is not arithmetic. Determine whether each sequence is Find the ratio of the consecutive terms. arithmetic. Write yes or no. 21. The common ratio is . SOLUTION: Subtract any term from the term directly after it. Since the ratios are the same, the sequence is geometric. ANSWER: Geometric; the common ratio is . There is no common difference. Therefore, the sequence is not arithmetic. 20. 12, 16, 20, 24, … ANSWER: SOLUTION: No To find the common difference, subtract any term from the term directly after it. 22. –9, –3, 0, 3, 9 SOLUTION: Subtract any term from the term directly after it. The common difference is 4. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. Since the ratios are not the same, the sequence is not ANSWER: geometric. No ANSWER: 23. 14, –5, –19, … Arithmetic; the common difference is 4. SOLUTION: Determine whether each sequence is Subtract any term from the term directly after it. arithmetic. Write yes or no. 21. There is no common difference. SOLUTION: Therefore, the sequence is not arithmetic. Subtract any term from the term directly after it. ANSWER: No 24. There is no common difference. Therefore, the sequence is not arithmetic. SOLUTION: Subtract any term from the term directly after it. ANSWER: No 22. –9, –3, 0, 3, 9 SOLUTION: The common difference is . Subtract any term from the term directly after it. Therefore, the sequence is arithmetic. ANSWER: Yes There is no common difference. Therefore, the sequence is not arithmetic. Find the next four terms of each arithmetic sequence. Then graph the sequence. ANSWER: No 25. –4, –1, 2, 5,… 23. 14, –5, –19, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. There is no common difference. To find the next term, add 3 to the last term. Therefore, the sequence is not arithmetic. 5 + 3 = 8 8 + 3 = 11 ANSWER: 11 + 3 = 14 No 14 + 3 = 17 Graph the sequence. 24. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is . 8, 11, 14, 17 Therefore, the sequence is arithmetic. ANSWER: Yes Find the next four terms of each arithmetic sequence. Then graph the sequence. 25. –4, –1, 2, 5,… SOLUTION: 26. 10, 2, –6, –14, … Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. The common difference is –8. To find the next term, add 3 to the last term. Therefore, this sequence is arithmetic. 5 + 3 = 8 To find the next term, add –8 to the last term. 8 + 3 = 11 11 + 3 = 14 14 + 3 = 17 –14 + (–8) = –22 –22 + (–8) = –30 –30 + (–8) = –38 Graph the sequence. –38 + (–8) = –46 Graph the sequence. ANSWER: 8, 11, 14, 17 ANSWER: –22, –30, –38, – 46 26. 10, 2, –6, –14, … 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. The common difference is –6. To find the next term, add –8 to the last term. Therefore, the sequence is arithmetic. –14 + (–8) = –22 To find the next term, add –6 to the last term. –22 + (–8) = –30 –30 + (–8) = –38 –23 + (–6) = –29 –38 + (–8) = –46 –29 + (–6) = –35 –35 + (–6) = –41 Graph the sequence. –41 + (–6) = –47 Graph the sequence. ANSWER: –22, –30, –38, – 46 ANSWER: –29, –35, – 41, – 47 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. 28. –19, –2, 15, … SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. The common difference is 17. –23 + (–6) = –29 Therefore, the sequence is arithmetic. –29 + (–6) = –35 –35 + (–6) = –41 To find the next term, add 17 to the last term. –41 + (–6) = –47 15 + 17 = 32 Graph the sequence. 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 Graph the sequence. ANSWER: –29, –35, – 41, – 47 ANSWER: 32, 49, 66, 83 28. –19, –2, 15, … SOLUTION: 29. Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 32 + 17 = 49 The common difference is . 49 + 17 = 66 66 + 17 = 83 Therefore, the sequence is arithmetic. Graph the sequence. To find the next term, add to the last term. ANSWER: Graph the sequence. 32, 49, 66, 83 ANSWER: 29. SOLUTION: Subtract any term from the term directly after it. The common difference is . Therefore, the sequence is arithmetic. 30. To find the next term, add to the last term. SOLUTION: Subtract any term from the term directly after it. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 30. SOLUTION: Subtract any term from the term directly after it. 31. THEATER There are 28 seats in the front row of a The common difference is –1. theater. Each successive row contains two more Therefore, the sequence is arithmetic. seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? To find the next term, add −1 to the last term. SOLUTION: Given a = 28, d = 2 and n = 24. 1 Find a . 24 Graph the sequence. ANSWER: 74 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? ANSWER: b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue indefinitely? Explain. SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Find a . 18 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, Therefore he will row for 30 minutes and 30 seconds how many seats are in the last row of the theater? on the 38th day. b. Given a = 5, d = 1.5 and a = 60. SOLUTION: 1 n Find n. Given a = 28, d = 2 and n = 24. 1 Find a . 24 Mario will first row an hour or more on the 38th day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be ANSWER: dedicated to rowing. 74 ANSWER: 32. CCSS SENSE-MAKING Mario began an exercise a. 30 minutes and 30 seconds program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and b. on the 38th day increase his rowing time by one minute and thirty seconds each day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be a. How long will he row on the 18th day? dedicated to rowing. b. On what day will Mario first row an hour or more? Determine whether each sequence is geometric. Write yes or no. c. Is it reasonable for this pattern to continue indefinitely? Explain. 33. 21, 14, 7, … SOLUTION: a. Given a = 5, d = 1.5 and n = 18. SOLUTION: 1 Find the ratio of the consecutive terms. Find a . 18 Since the ratios are not the same, the sequence is not geometric. Therefore he will row for 30 minutes and 30 seconds on the 38th day. ANSWER: No b. Given a = 5, d = 1.5 and a = 60. 1 n Find n. 34. 124, 186, 248, … SOLUTION: Find the ratio of the consecutive terms. Mario will first row an hour or more on the 38th day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be Since the ratios are not the same, the sequence is not dedicated to rowing. geometric. ANSWER: ANSWER: a. 30 minutes and 30 seconds No b. on the 38th day 35. –27, 18, –12, … c. Sample answer: It is unreasonable because there SOLUTION: are only so many hours in the day that can be dedicated to rowing. Find the ratio of the consecutive terms. Determine whether each sequence is Since the ratios are the same, the sequence is geometric. Write yes or no. geometric. ANSWER: 33. 21, 14, 7, … Yes 36. 162, 108, 72, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Since the ratios are same, the sequence is geometric. ANSWER: ANSWER: No Yes 34. 124, 186, 248, … 37. SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. ANSWER: No 35. –27, 18, –12, … Since the ratios are not same, the sequence is not SOLUTION: geometric. Find the ratio of the consecutive terms. ANSWER: Since the ratios are the same, the sequence is No geometric. ANSWER: 38. –4, –2, 0, 2, … Yes 36. 162, 108, 72, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are same, the sequence is geometric. ANSWER: No ANSWER: Yes Find the next three terms of the sequence. Then graph the sequence. 37. 39. 0.125, –0.5, 2, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. Since the ratios are not same, the sequence is not geometric. Graph the sequence. ANSWER: No 38. –4, –2, 0, 2, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are not same, the sequence is not – 8, 32, –128 geometric. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: 40. 18, 12, 8, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: – 8, 32, –128 ANSWER: 40. 18, 12, 8, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. 41. 64, 48, 36, … To find the next term, multiply the previous term by SOLUTION: . Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 41. 64, 48, 36, … SOLUTION: Find the ratio of the consecutive terms. 42. 81, 108, 144, … Since the ratios are same, the sequence is geometric. SOLUTION: To find the next term, multiply the previous term by Find the ratio of the consecutive terms. . Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. 43. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by SOLUTION: Find the ratio of the consecutive terms. . Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 27, 81, 243 43. SOLUTION: Find the ratio of the consecutive terms. 44. 1, 0.1, 0.01, 0.001, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. Graph the sequence. Graph the sequence. ANSWER: 27, 81, 243 ANSWER: 0.0001, 0.00001, 0.000001 44. 1, 0.1, 0.01, 0.001, … SOLUTION: Determine whether each sequence is Find the ratio of the consecutive terms. arithmetic, geometric, or neither. Explain your reasoning. 45. 3, 12, 27, 48, … Since the ratios are same, the sequence is geometric. SOLUTION: To find the next term, multiply the previous term by Subtract each term from the term directly after it. 0.1. There is no common difference. Graph the sequence. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. ANSWER: 0.0001, 0.00001, 0.000001 46. 1, –2, –5, –8, … SOLUTION: Subtract each term from the term directly after it. The common difference is –3. Therefore, the sequence is arithmetic. Determine whether each sequence is To find the common ratio, find the ratio of the arithmetic, geometric, or neither. Explain your consecutive terms. reasoning. 45. 3, 12, 27, 48, … Since the ratios are not same, the sequence is not SOLUTION: geometric. Subtract each term from the term directly after it. ANSWER: Arithmetic; the common difference is –3. There is no common difference. 47. 12, 36, 108, 324, … Therefore, the sequence is not arithmetic. SOLUTION: To find the common ratio, find the ratio of the Subtract each term from the term directly after it. consecutive terms. Since the ratios are not same, the sequence is not There is no common difference. geometric. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the ANSWER: consecutive terms. Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … The common ratio is 3. SOLUTION: Since the ratios are same, the sequence is geometric. Subtract each term from the term directly after it. ANSWER: Geometric; the common ratio is 3. The common difference is –3. Therefore, the sequence is arithmetic. 48. To find the common ratio, find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not geometric. ANSWER: There is no common difference. Therefore, this sequence is not arithmetic. Arithmetic; the common difference is –3. To find the common ratio, find the ratio of the 47. 12, 36, 108, 324, … consecutive terms. SOLUTION: Subtract each term from the term directly after it. The common ratio is . There is no common difference. Since the ratios are the same, the sequence is Therefore, this sequence is not arithmetic. geometric. To find the common ratio, find the ratio of the ANSWER: consecutive terms. Geometric; the common ratio is . The common ratio is 3. 49. Since the ratios are same, the sequence is geometric. SOLUTION: Subtract each term from the term directly after it. ANSWER: Geometric; the common ratio is 3. 48. The common difference is . SOLUTION: Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, this sequence is not arithmetic. Since the ratios are not same, the sequence is not To find the common ratio, find the ratio of the geometric. consecutive terms. ANSWER: Arithmetic; the common difference is . The common ratio is . 50. 6, 9, 14, 21, … Since the ratios are the same, the sequence is SOLUTION: geometric. Subtract each term from the term directly after it. ANSWER: Geometric; the common ratio is . There is no common difference. Therefore, the sequence is not arithmetic. 49. To find the common ratio, find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. The common difference is . Therefore, the sequence is arithmetic. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is To find the common ratio, find the ratio of the going to be on vacation for 8 days, what is the consecutive terms. minimum number of pages she needs to read per day to finish the book by the end of her vacation? SOLUTION: The number of pages to be read is 800 – 112 or 688. Since the ratios are not same, the sequence is not geometric. The minimum number of pages to read per day is . ANSWER: Arithmetic; the common difference is . ANSWER: 86 pg/day 50. 6, 9, 14, 21, … 52. DEPRECIATION Tammy’s car is expected to SOLUTION: depreciate at a rate of 15% per year. If her car is Subtract each term from the term directly after it. currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in There is no common difference. Therefore, the sequence is not arithmetic. then evaluate. To find the common ratio, find the ratio of the consecutive terms. The worth of the car will be about $9052 after 6 years. Since the ratios are not same, the sequence is not geometric. ANSWER: $9052 ANSWER: Neither; there is no common difference or ratio. 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, 51. READING Sareeta took an 800-page book on how thick would it be? vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day SOLUTION: to finish the book by the end of her vacation? Given a = 0.1, n = 37 and r = 2. 0 SOLUTION: Find a . 37 The number of pages to be read is 800 – 112 or 688. The minimum number of pages to read per day is . The thickness would be about 13,744 km. ANSWER: 86 pg/day ANSWER: about 13,744 km 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is 54. REASONING Explain why the sequence 8, 10, 13, currently valued at $24,000, to the nearest dollar, 17, 22 is not arithmetic. how much will it be worth in 6 years? SOLUTION: SOLUTION: Sample answer: The consecutive terms do not share Substitute 0.15, 6 and 24000 for r, t and P in a common difference. For instance, 22 – 17 = 5, then evaluate. while 17 – 13 = 4. ANSWER: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, The worth of the car will be about $9052 after 6 while 17 – 13 = 4. years. 55. OPEN ENDED Describe a real-life situation that ANSWER: can be represented by an arithmetic sequence with a $9052 common difference of 8. SOLUTION: 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of Sample answer: A babysitter earns $20 for cleaning paper that is 0.1 mm thick could be folded 37 times, the house and $8 extra for every hour she watches how thick would it be? the children. SOLUTION: ANSWER: Given a = 0.1, n = 37 and r = 2. Sample answer: A babysitter earns $20 for cleaning 0 the house and $8 extra for every hour she watches the children. Find a . 37 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: Let x be the first term in the arithmetic sequence. The thickness would be about 13,744 km. Therefore, the next two terms should be x + d and x + 2d. ANSWER: about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. SOLUTION: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: Sample answer: The consecutive terms do not share ANSWER: a common difference. For instance, 22 – 17 = 5, –3, 2, 7 while 17 – 13 = 4. 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is 55. OPEN ENDED Describe a real-life situation that arithmetic, geometric, neither, or both. Is either of can be represented by an arithmetic sequence with a them correct? Explain your reasoning. common difference of 8. SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: SOLUTION: Sample answer: Neither; the sequence is both Let x be the first term in the arithmetic sequence. arithmetic and geometric. Therefore, the next two terms should be x + d and x + 2d. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: –3, 2, 7 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. Determine whether each sequence is arithmetic no. ANSWER: 1. 8, –2, –12, –22 Yes SOLUTION: 3. 1, 2, 4, 8, 16 Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: There is no common difference. Yes Therefore, the sequence is not arithmetic. 2. –19, –12, –5, 2, 9 ANSWER: No SOLUTION: Subtract each term from the term directly after it. 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: There is no common difference. Yes Therefore, the sequence is not arithmetic. 3. 1, 2, 4, 8, 16 ANSWER: No SOLUTION: Subtract each term from the term directly after it. Find the next four terms of each arithmetic sequence. Then graph the sequence. 5. 6, 18, 30, … There is no common difference. SOLUTION: Therefore, the sequence is not arithmetic. Subtract each term from the term directly after it. ANSWER: No The common difference is 12. 4. 0.6, 0.9, 1.2, 1.8, ... Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. SOLUTION: 30 + 12 = 42 Subtract each term from the term directly after it. 42 + 12 = 54 54 + 12 = 66 66 + 12 = 78 Graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No Find the next four terms of each arithmetic sequence. Then graph the sequence. 5. 6, 18, 30, … ANSWER: 42, 54, 66, 78 SOLUTION: Subtract each term from the term directly after it. The common difference is 12. Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. 30 + 12 = 42 42 + 12 = 54 54 + 12 = 66 6. 15, 6, –3, … 66 + 12 = 78 SOLUTION: Graph the sequence. Subtract each term from the term directly after it. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add –9 to the last term. –3 + (–9) = –12 –12 + (–9) = –21 ANSWER: –21 + (–9) = –30 42, 54, 66, 78 –30 + (–9) = –39 Graph the sequence. 6. 15, 6, –3, … ANSWER: –12, –21, –30, –39 SOLUTION: Subtract each term from the term directly after it. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add –9 to the last term. 7. –19, –11, –3, … –3 + (–9) = –12 –12 + (–9) = –21 SOLUTION: –21 + (–9) = –30 Subtract each term from the term directly after it. –30 + (–9) = –39 Graph the sequence. The common difference is 8. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 ANSWER: –12, –21, –30, –39 Graph the sequence. 7. –19, –11, –3, … ANSWER: 5, 13, 21, 29 SOLUTION: Subtract each term from the term directly after it. The common difference is 8. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. 8. –26, –33, –40, … –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 SOLUTION: 21 + 8 = 29 Subtract each term from the term directly after it. Graph the sequence. The common difference is –7. Therefore, the sequence is arithmetic. To find the next term, add –7 to the last term. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 ANSWER: –61 + (–7) = –68 5, 13, 21, 29 Graph the sequence. 8. –26, –33, –40, … ANSWER: –47, –54, –61, –68 SOLUTION: Subtract each term from the term directly after it. The common difference is –7. Therefore, the sequence is arithmetic. To find the next term, add –7 to the last term. 9. FINANCIAL LITERACY Kelly is saving her –40 + (–7) = –47 money to buy a car. She has $250, and she plans to –47 + (–7) = –54 save $75 per week from her job as a waitress. –54 + (–7) = –61 –61 + (–7) = –68 a. How much will Kelly have saved after 8 weeks? Graph the sequence. b. If the car costs $2000, how long will it take her to save enough money at this rate? SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. b. Given a = 2000. n Find n. ANSWER: –47, –54, –61, –68 So, it will take about 24 weeks to save $2000. ANSWER: a. $850 b. 24 wk 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. Determine whether each sequence is geometric. Write yes or no. a. How much will Kelly have saved after 8 weeks? 10. –8, –5, –1, 4, … b. If the car costs $2000, how long will it take her to save enough money at this rate? SOLUTION: Find the ratio of the consecutive terms. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. b. Given a = 2000. Since the ratios are not same, the sequence is not n geometric. Find n. ANSWER: No 11. 4, 12, 36, 108, … So, it will take about 24 weeks to save $2000. SOLUTION: ANSWER: Find the ratio of the consecutive terms. a. $850 b. 24 wk Since the ratios are the same, the sequence is Determine whether each sequence is geometric. geometric. Write yes or no. 10. –8, –5, –1, 4, … ANSWER: Yes SOLUTION: Find the ratio of the consecutive terms. 12. 27, 9, 3, 1, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: Since the ratios are the same, the sequence is No geometric. ANSWER: 11. 4, 12, 36, 108, … Yes SOLUTION: 13. 7, 14, 21, 28, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are not the same, the sequence is not ANSWER: geometric. Yes ANSWER: 12. 27, 9, 3, 1, … No SOLUTION: Find the next three terms of each geometric Find the ratio of the consecutive terms. sequence. Then graph the sequence. 14. 8, 12, 18, 27, … Since the ratios are the same, the sequence is SOLUTION: geometric. Find the ratio of the consecutive terms. ANSWER: Yes Since the ratios are the same, the sequence is geometric 13. 7, 14, 21, 28, … To find the next term, multiply the previous term by SOLUTION: . Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. ANSWER: Graph the sequence. No Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: 40.5, 60.75, 91.125 Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . 15. 8, 16, 32, 64, … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 2. ANSWER: 40.5, 60.75, 91.125 Graph the sequence. 15. 8, 16, 32, 64, … ANSWER: SOLUTION: 128, 256, 512 Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 2. 16. 250, 50, 10, 2, … SOLUTION: Graph the sequence. Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . ANSWER: 128, 256, 512 Graph the sequence. 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . Graph the sequence. 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: To find the next term, multiply the previous term by . Graph the sequence. 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . Determine whether each sequence is arithmetic, geometric, or neither. Explain your Graph the sequence. reasoning. 18. 5, 1, 7, 3, 9, … SOLUTION: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. ANSWER: Since the ratios are not the same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … SOLUTION: Determine whether each sequence is arithmetic, geometric, or neither. Explain your To find the common difference, subtract any term reasoning. from the term directly after it. 18. 5, 1, 7, 3, 9, … SOLUTION: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. The common ratio is . Since the ratios are the same, the sequence is Since the ratios are not the same, the sequence is not geometric. geometric. ANSWER: ANSWER: Neither; there is no common difference or ratio. Geometric; the common ratio is . 10-1 Sequences as Functions 19. 200, –100, 50, –25, … 20. 12, 16, 20, 24, … SOLUTION: SOLUTION: To find the common difference, subtract any term To find the common difference, subtract any term from the term directly after it. from the term directly after it. There is no common difference. The common difference is 4. Therefore, the sequence is not arithmetic. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. The common ratio is . Since the ratios are not the same, the sequence is not geometric. Since the ratios are the same, the sequence is geometric. ANSWER: Arithmetic; the common difference is 4. ANSWER: Determine whether each sequence is Geometric; the common ratio is . arithmetic. Write yes or no. 20. 12, 16, 20, 24, … 21. SOLUTION: SOLUTION: To find the common difference, subtract any term Subtract any term from the term directly after it. from the term directly after it. The common difference is 4. Therefore, the sequence is arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. ANSWER: No Since the ratios are not the same, the sequence is not geometric. 22. –9, –3, 0, 3, 9 eSolutionsManual-PoweredbyCognero Page8 ANSWER: SOLUTION: Arithmetic; the common difference is 4. Subtract any term from the term directly after it. Determine whether each sequence is arithmetic. Write yes or no. There is no common difference. 21. Therefore, the sequence is not arithmetic. SOLUTION: ANSWER: Subtract any term from the term directly after it. No 23. 14, –5, –19, … SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: There is no common difference. No Therefore, the sequence is not arithmetic. 22. –9, –3, 0, 3, 9 ANSWER: No SOLUTION: Subtract any term from the term directly after it. 24. SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No 23. 14, –5, –19, … The common difference is . Therefore, the sequence is arithmetic. SOLUTION: Subtract any term from the term directly after it. ANSWER: Yes Find the next four terms of each arithmetic There is no common difference. sequence. Then graph the sequence. Therefore, the sequence is not arithmetic. 25. –4, –1, 2, 5,… ANSWER: SOLUTION: No Subtract any term from the term directly after it. 24. The common difference is 3. SOLUTION: Therefore, the sequence is arithmetic. Subtract any term from the term directly after it. To find the next term, add 3 to the last term. 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 14 + 3 = 17 The common difference is . Graph the sequence. Therefore, the sequence is arithmetic. ANSWER: Yes Find the next four terms of each arithmetic sequence. Then graph the sequence. 25. –4, –1, 2, 5,… ANSWER: SOLUTION: 8, 11, 14, 17 Subtract any term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. To find the next term, add 3 to the last term. 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 26. 10, 2, –6, –14, … 14 + 3 = 17 Graph the sequence. SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. –14 + (–8) = –22 –22 + (–8) = –30 ANSWER: –30 + (–8) = –38 8, 11, 14, 17 –38 + (–8) = –46 Graph the sequence. 26. 10, 2, –6, –14, … ANSWER: SOLUTION: –22, –30, –38, – 46 Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. –14 + (–8) = –22 –22 + (–8) = –30 –30 + (–8) = –38 27. –5, –11, –17, –23, … –38 + (–8) = –46 SOLUTION: Graph the sequence. Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. –23 + (–6) = –29 –29 + (–6) = –35 ANSWER: –35 + (–6) = –41 –22, –30, –38, – 46 –41 + (–6) = –47 Graph the sequence. 27. –5, –11, –17, –23, … SOLUTION: ANSWER: Subtract any term from the term directly after it. –29, –35, – 41, – 47 The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. –23 + (–6) = –29 –29 + (–6) = –35 –35 + (–6) = –41 –41 + (–6) = –47 28. –19, –2, 15, … Graph the sequence. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 ANSWER: 32 + 17 = 49 –29, –35, – 41, – 47 49 + 17 = 66 66 + 17 = 83 Graph the sequence. 28. –19, –2, 15, … ANSWER: SOLUTION: 32, 49, 66, 83 Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 32 + 17 = 49 49 + 17 = 66 29. 66 + 17 = 83 Graph the sequence. SOLUTION: Subtract any term from the term directly after it. The common difference is . Therefore, the sequence is arithmetic. ANSWER: 32, 49, 66, 83 To find the next term, add to the last term. Graph the sequence. 29. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is . Therefore, the sequence is arithmetic. To find the next term, add to the last term. 30. Graph the sequence. SOLUTION: Subtract any term from the term directly after it. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. ANSWER: Graph the sequence. 30. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more Graph the sequence. seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: Given a = 28, d = 2 and n = 24. 1 Find a . 24 ANSWER: ANSWER: 74 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or 31. THEATER There are 28 seats in the front row of a more? theater. Each successive row contains two more seats than the previous row. If there are 24 rows, c. Is it reasonable for this pattern to continue how many seats are in the last row of the theater? indefinitely? Explain. SOLUTION: SOLUTION: Given a1 = 28, d = 2 and n = 24. a. Given a = 5, d = 1.5 and n = 18. 1 Find a24. Find a . 18 Therefore he will row for 30 minutes and 30 seconds on the 38th day. ANSWER: 74 b. Given a = 5, d = 1.5 and a = 60. 1 n Find n. 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? Mario will first row an hour or more on the 38th day. b. On what day will Mario first row an hour or c. Sample answer: It is unreasonable because there more? are only so many hours in the day that can be dedicated to rowing. c. Is it reasonable for this pattern to continue indefinitely? Explain. ANSWER: a. 30 minutes and 30 seconds SOLUTION: a. Given a = 5, d = 1.5 and n = 18. b. on the 38th day 1 Find a . c. Sample answer: It is unreasonable because there 18 are only so many hours in the day that can be dedicated to rowing. Determine whether each sequence is geometric. Write yes or no. Therefore he will row for 30 minutes and 30 seconds on the 38th day. 33. 21, 14, 7, … b. Given a = 5, d = 1.5 and a = 60. 1 n Find n. SOLUTION: Find the ratio of the consecutive terms. Mario will first row an hour or more on the 38th day. Since the ratios are not the same, the sequence is not geometric. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing. ANSWER: No ANSWER: a. 30 minutes and 30 seconds 34. 124, 186, 248, … b. on the 38th day SOLUTION: c. Sample answer: It is unreasonable because there Find the ratio of the consecutive terms. are only so many hours in the day that can be dedicated to rowing. Determine whether each sequence is Since the ratios are not the same, the sequence is not geometric. Write yes or no. geometric. 33. 21, 14, 7, … ANSWER: No SOLUTION: Find the ratio of the consecutive terms. 35. –27, 18, –12, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not Since the ratios are the same, the sequence is geometric. geometric. ANSWER: ANSWER: Yes No 36. 162, 108, 72, … 34. 124, 186, 248, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. Since the ratios are not the same, the sequence is not geometric. ANSWER: Yes ANSWER: No 37. 35. –27, 18, –12, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Yes 36. 162, 108, 72, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: No Since the ratios are same, the sequence is geometric. 38. –4, –2, 0, 2, … ANSWER: Yes SOLUTION: Find the ratio of the consecutive terms. 37. SOLUTION: Since the ratios are not same, the sequence is not Find the ratio of the consecutive terms. geometric. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: Since the ratios are not same, the sequence is not geometric. Find the ratio of the consecutive terms. ANSWER: No Since the ratios are same, the sequence is geometric 38. –4, –2, 0, 2, … To find the next term, multiply the previous term with −4. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not Graph the sequence. geometric. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. 39. 0.125, –0.5, 2, … ANSWER: SOLUTION: – 8, 32, –128 Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. 40. 18, 12, 8, … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: – 8, 32, –128 Graph the sequence. 40. 18, 12, 8, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . 41. 64, 48, 36, … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 41. 64, 48, 36, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . 42. 81, 108, 144, … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . 43. Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. ANSWER: Graph the sequence. 43. SOLUTION: ANSWER: Find the ratio of the consecutive terms. 27, 81, 243 Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. 44. 1, 0.1, 0.01, 0.001, … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. ANSWER: 27, 81, 243 Graph the sequence. 44. 1, 0.1, 0.01, 0.001, … ANSWER: SOLUTION: 0.0001, 0.00001, 0.000001 Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. Determine whether each sequence is arithmetic, geometric, or neither. Explain your Graph the sequence. reasoning. 45. 3, 12, 27, 48, … SOLUTION: Subtract each term from the term directly after it. There is no common difference. ANSWER: Therefore, the sequence is not arithmetic. 0.0001, 0.00001, 0.000001 To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. Determine whether each sequence is arithmetic, geometric, or neither. Explain your 46. 1, –2, –5, –8, … reasoning. 45. 3, 12, 27, 48, … SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. The common difference is –3. Therefore, the sequence is arithmetic. There is no common difference. To find the common ratio, find the ratio of the consecutive terms. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are not same, the sequence is not ANSWER: geometric. Arithmetic; the common difference is –3. ANSWER: 47. 12, 36, 108, 324, … Neither; there is no common difference or ratio. SOLUTION: 46. 1, –2, –5, –8, … Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the The common difference is –3. consecutive terms. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common ratio is 3. Since the ratios are same, the sequence is geometric. Since the ratios are not same, the sequence is not geometric. ANSWER: Geometric; the common ratio is 3. ANSWER: Arithmetic; the common difference is –3. 48. 47. 12, 36, 108, 324, … SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. There is no common difference. There is no common difference. Therefore, this sequence is not arithmetic. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the To find the common ratio, find the ratio of the consecutive terms. consecutive terms. The common ratio is 3. The common ratio is . Since the ratios are same, the sequence is geometric. Since the ratios are the same, the sequence is ANSWER: geometric. Geometric; the common ratio is 3. ANSWER: Geometric; the common ratio is . 48. SOLUTION: 49. Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common difference is . Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common ratio is . Since the ratios are the same, the sequence is geometric. Since the ratios are not same, the sequence is not ANSWER: geometric. Geometric; the common ratio is . ANSWER: Arithmetic; the common difference is . 49. 50. 6, 9, 14, 21, … SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. There is no common difference. The common difference is . Therefore, the sequence is not arithmetic. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. ANSWER: 51. READING Sareeta took an 800-page book on Arithmetic; the common difference is . vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day 50. 6, 9, 14, 21, … to finish the book by the end of her vacation? SOLUTION: SOLUTION: Subtract each term from the term directly after it. The number of pages to be read is 800 – 112 or 688. The minimum number of pages to read per day is . There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: To find the common ratio, find the ratio of the consecutive terms. 86 pg/day 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, Since the ratios are not same, the sequence is not how much will it be worth in 6 years? geometric. SOLUTION: ANSWER: Substitute 0.15, 6 and 24000 for r, t and P in Neither; there is no common difference or ratio. then evaluate. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation? The worth of the car will be about $9052 after 6 years. SOLUTION: ANSWER: The number of pages to be read is 800 – 112 or 688. $9052 The minimum number of pages to read per day is . 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, how thick would it be? ANSWER: 86 pg/day SOLUTION: Given a = 0.1, n = 37 and r = 2. 0 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is Find a37. currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in then evaluate. The thickness would be about 13,744 km. ANSWER: about 13,744 km The worth of the car will be about $9052 after 6 years. 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. ANSWER: $9052 SOLUTION: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, 53. CCSS REGULARITY When a piece of paper is while 17 – 13 = 4. folded onto itself, it doubles in thickness. If a piece of paper that is 0.1 mm thick could be folded 37 times, how thick would it be? ANSWER: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, SOLUTION: while 17 – 13 = 4. Given a = 0.1, n = 37 and r = 2. 0 Find a . 55. OPEN ENDED Describe a real-life situation that 37 can be represented by an arithmetic sequence with a common difference of 8. SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. The thickness would be about 13,744 km. ANSWER: ANSWER: Sample answer: A babysitter earns $20 for cleaning about 13,744 km the house and $8 extra for every hour she watches the children. 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the SOLUTION: terms is –42. Find the terms. Sample answer: The consecutive terms do not share SOLUTION: a common difference. For instance, 22 – 17 = 5, Let x be the first term in the arithmetic sequence. while 17 – 13 = 4. Therefore, the next two terms should be x + d and x + 2d. ANSWER: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. SOLUTION: Sample answer: Sample answer: A babysitter earns $20 for cleaning Let d = 5. the house and $8 extra for every hour she watches the children. Therefore, the terms are –3, 2, 7. ANSWER: ANSWER: –3, 2, 7 Sample answer: A babysitter earns $20 for cleaning 57. ERROR ANALYSIS Brody and Gen are the house and $8 extra for every hour she watches determining whether the sequence 8, 8, 8,… is the children. arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: ANSWER: Sample answer: Neither; the sequence is both –3, 2, 7 arithmetic and geometric. 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is 58. OPEN ENDED Find a geometric sequence, an arithmetic, geometric, neither, or both. Is either of arithmetic sequence, and a sequence that is neither them correct? Explain your reasoning. geometric nor arithmetic that begins 3, 9,… . SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Yes Determine whether each sequence is arithmetic no. 3. 1, 2, 4, 8, 16 1. 8, –2, –12, –22 SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is –10. There is no common difference. Therefore, the sequence is arithmetic. Therefore, the sequence is not arithmetic. ANSWER: ANSWER: Yes No 2. –19, –12, –5, 2, 9 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is 7. There is no common difference. Therefore, the sequence is arithmetic. Therefore, the sequence is not arithmetic. ANSWER: ANSWER: Yes No 3. 1, 2, 4, 8, 16 Find the next four terms of each arithmetic sequence. Then graph the sequence. SOLUTION: 5. 6, 18, 30, … Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. The common difference is 12. ANSWER: Therefore, the sequence is arithmetic. No To find the next term, add 12 to the last term. 30 + 12 = 42 4. 0.6, 0.9, 1.2, 1.8, ... 42 + 12 = 54 54 + 12 = 66 66 + 12 = 78 SOLUTION: Subtract each term from the term directly after it. Graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No Find the next four terms of each arithmetic ANSWER: sequence. Then graph the sequence. 42, 54, 66, 78 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. The common difference is 12. Therefore, the sequence is arithmetic. 6. 15, 6, –3, … To find the next term, add 12 to the last term. 30 + 12 = 42 SOLUTION: 42 + 12 = 54 54 + 12 = 66 Subtract each term from the term directly after it. 66 + 12 = 78 Graph the sequence. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add –9 to the last term. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 Graph the sequence. ANSWER: 42, 54, 66, 78 ANSWER: –12, –21, –30, –39 6. 15, 6, –3, … SOLUTION: Subtract each term from the term directly after it. The common difference is –9. 7. –19, –11, –3, … Therefore, the sequence is arithmetic. SOLUTION: To find the next term, add –9 to the last term. Subtract each term from the term directly after it. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 The common difference is 8. Graph the sequence. Therefore, the sequence is arithmetic. To find the next term, add 8 to the last term. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. ANSWER: –12, –21, –30, –39 ANSWER: 5, 13, 21, 29 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. The common difference is 8. Therefore, the sequence is arithmetic. 8. –26, –33, –40, … To find the next term, add 8 to the last term. SOLUTION: Subtract each term from the term directly after it. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. The common difference is –7. Therefore, the sequence is arithmetic. To find the next term, add –7 to the last term. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 –61 + (–7) = –68 Graph the sequence. ANSWER: 5, 13, 21, 29 ANSWER: –47, –54, –61, –68 8. –26, –33, –40, … SOLUTION: Subtract each term from the term directly after it. The common difference is –7. Therefore, the sequence is arithmetic. 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to To find the next term, add –7 to the last term. save $75 per week from her job as a waitress. –40 + (–7) = –47 a. How much will Kelly have saved after 8 weeks? –47 + (–7) = –54 –54 + (–7) = –61 b. If the car costs $2000, how long will it take her to –61 + (–7) = –68 save enough money at this rate? Graph the sequence. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. b. Given a = 2000. n Find n. ANSWER: –47, –54, –61, –68 So, it will take about 24 weeks to save $2000. ANSWER: a. $850 b. 24 wk Determine whether each sequence is 9. FINANCIAL LITERACY Kelly is saving her geometric. Write yes or no. money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. 10. –8, –5, –1, 4, … a. How much will Kelly have saved after 8 weeks? SOLUTION: Find the ratio of the consecutive terms. b. If the car costs $2000, how long will it take her to save enough money at this rate? SOLUTION: a. Given a = 250, d = 75 and n = 8. Since the ratios are not same, the sequence is not 0 geometric. After 8 weeks, she will have 250 + (8 × 75) or $850. b. Given a = 2000. ANSWER: n No Find n. 11. 4, 12, 36, 108, … SOLUTION: Find the ratio of the consecutive terms. So, it will take about 24 weeks to save $2000. ANSWER: a. $850 Since the ratios are the same, the sequence is geometric. b. 24 wk ANSWER: Determine whether each sequence is Yes geometric. Write yes or no. 10. –8, –5, –1, 4, … 12. 27, 9, 3, 1, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not Since the ratios are the same, the sequence is geometric. geometric. ANSWER: ANSWER: No Yes 13. 7, 14, 21, 28, … 11. 4, 12, 36, 108, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not Since the ratios are the same, the sequence is geometric. geometric. ANSWER: ANSWER: No Yes Find the next three terms of each geometric 12. 27, 9, 3, 1, … sequence. Then graph the sequence. SOLUTION: 14. 8, 12, 18, 27, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Since the ratios are the same, the sequence is geometric ANSWER: Yes To find the next term, multiply the previous term by . 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Graph the sequence. ANSWER: No Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … SOLUTION: ANSWER: Find the ratio of the consecutive terms. 40.5, 60.75, 91.125 Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 2. ANSWER: Graph the sequence. 40.5, 60.75, 91.125 ANSWER: 128, 256, 512 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by 16. 250, 50, 10, 2, … 2. SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . ANSWER: 128, 256, 512 Graph the sequence. 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by . 17. 9, –3, 1, , … Graph the sequence. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. ANSWER: Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 18. 5, 1, 7, 3, 9, … Graph the sequence. SOLUTION: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. ANSWER: Since the ratios are not the same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. There is no common difference. 18. 5, 1, 7, 3, 9, … Therefore, the sequence is not arithmetic. SOLUTION: Find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. The common ratio is . Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Since the ratios are not the same, the sequence is not geometric. Geometric; the common ratio is . ANSWER: 20. 12, 16, 20, 24, … Neither; there is no common difference or ratio. SOLUTION: 19. 200, –100, 50, –25, … To find the common difference, subtract any term from the term directly after it. SOLUTION: To find the common difference, subtract any term from the term directly after it. The common difference is 4. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. The common ratio is . ANSWER: Arithmetic; the common difference is 4. Since the ratios are the same, the sequence is geometric. Determine whether each sequence is arithmetic. Write yes or no. ANSWER: 21. Geometric; the common ratio is . SOLUTION: 20. 12, 16, 20, 24, … Subtract any term from the term directly after it. SOLUTION: To find the common difference, subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. The common difference is 4. Therefore, the sequence is arithmetic. ANSWER: No Find the ratio of the consecutive terms. 22. –9, –3, 0, 3, 9 Since the ratios are not the same, the sequence is not SOLUTION: geometric. Subtract any term from the term directly after it. ANSWER: Arithmetic; the common difference is 4. There is no common difference. Determine whether each sequence is Therefore, the sequence is not arithmetic. arithmetic. Write yes or no. ANSWER: 21. No SOLUTION: 23. 14, –5, –19, … Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. There is no common difference. There is no common difference. Therefore, the sequence is not arithmetic. Therefore, the sequence is not arithmetic. ANSWER: ANSWER: No 10-1 Sequences as Functions No 22. –9, –3, 0, 3, 9 24. SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: The common difference is . No Therefore, the sequence is arithmetic. 23. 14, –5, –19, … ANSWER: Yes SOLUTION: Subtract any term from the term directly after it. Find the next four terms of each arithmetic sequence. Then graph the sequence. 25. –4, –1, 2, 5,… There is no common difference. Therefore, the sequence is not arithmetic. SOLUTION: Subtract any term from the term directly after it. ANSWER: No The common difference is 3. 24. Therefore, the sequence is arithmetic. To find the next term, add 3 to the last term. SOLUTION: Subtract any term from the term directly after it. 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 14 + 3 = 17 Graph the sequence. The common difference is . Therefore, the sequence is arithmetic. eSolutionsManual-PoweredbyCognero Page9 ANSWER: Yes Find the next four terms of each arithmetic sequence. Then graph the sequence. ANSWER: 8, 11, 14, 17 25. –4, –1, 2, 5,… SOLUTION: Subtract any term from the term directly after it. The common difference is 3. Therefore, the sequence is arithmetic. To find the next term, add 3 to the last term. 26. 10, 2, –6, –14, … 5 + 3 = 8 8 + 3 = 11 SOLUTION: 11 + 3 = 14 Subtract any term from the term directly after it. 14 + 3 = 17 Graph the sequence. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. –14 + (–8) = –22 –22 + (–8) = –30 –30 + (–8) = –38 –38 + (–8) = –46 ANSWER: Graph the sequence. 8, 11, 14, 17 ANSWER: –22, –30, –38, – 46 26. 10, 2, –6, –14, … SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. To find the next term, add –8 to the last term. 27. –5, –11, –17, –23, … –14 + (–8) = –22 SOLUTION: –22 + (–8) = –30 Subtract any term from the term directly after it. –30 + (–8) = –38 –38 + (–8) = –46 Graph the sequence. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. –23 + (–6) = –29 –29 + (–6) = –35 –35 + (–6) = –41 –41 + (–6) = –47 Graph the sequence. ANSWER: –22, –30, –38, – 46 ANSWER: 27. –5, –11, –17, –23, … –29, –35, – 41, – 47 SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. –23 + (–6) = –29 28. –19, –2, 15, … –29 + (–6) = –35 –35 + (–6) = –41 SOLUTION: –41 + (–6) = –47 Subtract any term from the term directly after it. Graph the sequence. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 ANSWER: Graph the sequence. –29, –35, – 41, – 47 ANSWER: 32, 49, 66, 83 28. –19, –2, 15, … SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 29. 15 + 17 = 32 32 + 17 = 49 49 + 17 = 66 SOLUTION: 66 + 17 = 83 Subtract any term from the term directly after it. Graph the sequence. The common difference is . Therefore, the sequence is arithmetic. To find the next term, add to the last term. ANSWER: 32, 49, 66, 83 Graph the sequence. 29. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is . Therefore, the sequence is arithmetic. To find the next term, add to the last term. 30. SOLUTION: Subtract any term from the term directly after it. Graph the sequence. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. ANSWER: Graph the sequence. 30. SOLUTION: Subtract any term from the term directly after it. ANSWER: The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? Graph the sequence. SOLUTION: Given a = 28, d = 2 and n = 24. 1 Find a . 24 ANSWER: ANSWER: 74 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue indefinitely? Explain. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, SOLUTION: how many seats are in the last row of the theater? a. Given a = 5, d = 1.5 and n = 18. 1 SOLUTION: Find a . 18 Given a = 28, d = 2 and n = 24. 1 Find a . 24 Therefore he will row for 30 minutes and 30 seconds on the 38th day. b. Given a = 5, d = 1.5 and a = 60. 1 n Find n. ANSWER: 74 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and Mario will first row an hour or more on the 38th day. increase his rowing time by one minute and thirty seconds each day. c. Sample answer: It is unreasonable because there are only so many hours in the day that can be a. How long will he row on the 18th day? dedicated to rowing. b. On what day will Mario first row an hour or more? ANSWER: a. 30 minutes and 30 seconds c. Is it reasonable for this pattern to continue indefinitely? Explain. b. on the 38th day c. Sample answer: It is unreasonable because there SOLUTION: are only so many hours in the day that can be a. Given a = 5, d = 1.5 and n = 18. 1 dedicated to rowing. Find a . 18 Determine whether each sequence is geometric. Write yes or no. 33. 21, 14, 7, … Therefore he will row for 30 minutes and 30 seconds on the 38th day. SOLUTION: Find the ratio of the consecutive terms. b. Given a = 5, d = 1.5 and a = 60. 1 n Find n. Since the ratios are not the same, the sequence is not geometric. Mario will first row an hour or more on the 38th day. ANSWER: No c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing. 34. 124, 186, 248, … ANSWER: SOLUTION: a. 30 minutes and 30 seconds Find the ratio of the consecutive terms. b. on the 38th day c. Sample answer: It is unreasonable because there are only so many hours in the day that can be Since the ratios are not the same, the sequence is not dedicated to rowing. geometric. Determine whether each sequence is ANSWER: geometric. Write yes or no. No 33. 21, 14, 7, … 35. –27, 18, –12, … SOLUTION: SOLUTION: Find the ratio of the consecutive terms. Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Since the ratios are not the same, the sequence is not geometric. Yes 36. 162, 108, 72, … ANSWER: No SOLUTION: Find the ratio of the consecutive terms. 34. 124, 186, 248, … SOLUTION: Since the ratios are same, the sequence is geometric. Find the ratio of the consecutive terms. ANSWER: Yes Since the ratios are not the same, the sequence is not geometric. 37. ANSWER: No SOLUTION: Find the ratio of the consecutive terms. 35. –27, 18, –12, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Yes 36. 162, 108, 72, … Since the ratios are not same, the sequence is not geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: No 38. –4, –2, 0, 2, … Since the ratios are same, the sequence is geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: Yes 37. Since the ratios are not same, the sequence is not geometric. SOLUTION: ANSWER: Find the ratio of the consecutive terms. No Find the next three terms of the sequence. Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are same, the sequence is geometric ANSWER: To find the next term, multiply the previous term with No −4. 38. –4, –2, 0, 2, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: No Find the next three terms of the sequence. Then graph the sequence. ANSWER: – 8, 32, –128 39. 0.125, –0.5, 2, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term with −4. 40. 18, 12, 8, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: – 8, 32, –128 Graph the sequence. 40. 18, 12, 8, … SOLUTION: ANSWER: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . 41. 64, 48, 36, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 41. 64, 48, 36, … ANSWER: SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by . 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . ANSWER: Graph the sequence. 42. 81, 108, 144, … ANSWER: SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . 43. SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. ANSWER: Graph the sequence. ANSWER: 43. 27, 81, 243 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. 44. 1, 0.1, 0.01, 0.001, … SOLUTION: Find the ratio of the consecutive terms. Graph the sequence. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. Graph the sequence. ANSWER: 27, 81, 243 ANSWER: 0.0001, 0.00001, 0.000001 44. 1, 0.1, 0.01, 0.001, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by 0.1. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 45. 3, 12, 27, 48, … Graph the sequence. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. ANSWER: 0.0001, 0.00001, 0.000001 Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … Determine whether each sequence is SOLUTION: arithmetic, geometric, or neither. Explain your Subtract each term from the term directly after it. reasoning. 45. 3, 12, 27, 48, … SOLUTION: The common difference is –3. Subtract each term from the term directly after it. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, the sequence is not arithmetic. Since the ratios are not same, the sequence is not To find the common ratio, find the ratio of the geometric. consecutive terms. ANSWER: Arithmetic; the common difference is –3. Since the ratios are not same, the sequence is not 47. 12, 36, 108, 324, … geometric. SOLUTION: ANSWER: Subtract each term from the term directly after it. Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … There is no common difference. SOLUTION: Therefore, this sequence is not arithmetic. Subtract each term from the term directly after it. To find the common ratio, find the ratio of the consecutive terms. The common difference is –3. Therefore, the sequence is arithmetic. The common ratio is 3. To find the common ratio, find the ratio of the Since the ratios are same, the sequence is geometric. consecutive terms. ANSWER: Geometric; the common ratio is 3. Since the ratios are not same, the sequence is not geometric. 48. ANSWER: Arithmetic; the common difference is –3. SOLUTION: Subtract each term from the term directly after it. 47. 12, 36, 108, 324, … SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the There is no common difference. consecutive terms. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common ratio is . The common ratio is 3. Since the ratios are the same, the sequence is geometric. Since the ratios are same, the sequence is geometric. ANSWER: ANSWER: Geometric; the common ratio is 3. Geometric; the common ratio is . 49. 48. SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. There is no common difference. Therefore, this sequence is not arithmetic. The common difference is . To find the common ratio, find the ratio of the Therefore, the sequence is arithmetic. consecutive terms. To find the common ratio, find the ratio of the consecutive terms. The common ratio is . Since the ratios are not same, the sequence is not Since the ratios are the same, the sequence is geometric. geometric. ANSWER: ANSWER: Arithmetic; the common difference is . Geometric; the common ratio is . 50. 6, 9, 14, 21, … 49. SOLUTION: Subtract each term from the term directly after it. SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. The common difference is . Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. Since the ratios are not same, the sequence is not geometric. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the ANSWER: minimum number of pages she needs to read per day to finish the book by the end of her vacation? Arithmetic; the common difference is . SOLUTION: 50. 6, 9, 14, 21, … The number of pages to be read is 800 – 112 or 688. The minimum number of pages to read per day is SOLUTION: Subtract each term from the term directly after it. . ANSWER: There is no common difference. 86 pg/day Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the 52. DEPRECIATION Tammy’s car is expected to consecutive terms. depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? SOLUTION: Since the ratios are not same, the sequence is not Substitute 0.15, 6 and 24000 for r, t and P in geometric. then evaluate. ANSWER: Neither; there is no common difference or ratio. 51. READING Sareeta took an 800-page book on The worth of the car will be about $9052 after 6 vacation. If she was already on page 112 and is years. going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation? ANSWER: $9052 SOLUTION: The number of pages to be read is 800 – 112 or 688. 53. CCSS REGULARITY When a piece of paper is folded onto itself, it doubles in thickness. If a piece of The minimum number of pages to read per day is paper that is 0.1 mm thick could be folded 37 times, how thick would it be? . SOLUTION: Given a = 0.1, n = 37 and r = 2. 0 ANSWER: 86 pg/day Find a . 37 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? The thickness would be about 13,744 km. SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in ANSWER: then evaluate. about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. The worth of the car will be about $9052 after 6 years. SOLUTION: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, ANSWER: while 17 – 13 = 4. $9052 ANSWER: 53. CCSS REGULARITY When a piece of paper is Sample answer: The consecutive terms do not share folded onto itself, it doubles in thickness. If a piece of a common difference. For instance, 22 – 17 = 5, paper that is 0.1 mm thick could be folded 37 times, while 17 – 13 = 4. how thick would it be? 55. OPEN ENDED Describe a real-life situation that SOLUTION: can be represented by an arithmetic sequence with a Given a = 0.1, n = 37 and r = 2. 0 common difference of 8. Find a . 37 SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. ANSWER: The thickness would be about 13,744 km. Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. ANSWER: about 13,744 km 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the 54. REASONING Explain why the sequence 8, 10, 13, terms is –42. Find the terms. 17, 22 is not arithmetic. SOLUTION: Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x SOLUTION: + 2d. Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. ANSWER: Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. SOLUTION: ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches –3, 2, 7 the children. 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of ANSWER: them correct? Explain your reasoning. Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. SOLUTION: Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Sample answer: Neither; the sequence is both Let d = 5. arithmetic and geometric. Therefore, the terms are –3, 2, 7. ANSWER: 58. OPEN ENDED Find a geometric sequence, an –3, 2, 7 arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Determine whether each sequence is arithmetic no. 1. 8, –2, –12, –22 SOLUTION: Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. ANSWER: Yes 2. –19, –12, –5, 2, 9 SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: Yes 3. 1, 2, 4, 8, 16 SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. Determine whether each sequence is arithmetic ANSWER: no. No 1. 8, –2, –12, –22 4. 0.6, 0.9, 1.2, 1.8, ... SOLUTION: SOLUTION: Subtract each term from the term directly after it. Subtract each term from the term directly after it. The common difference is –10. Therefore, the sequence is arithmetic. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: Yes ANSWER: No 2. –19, –12, –5, 2, 9 Find the next four terms of each arithmetic sequence. Then graph the sequence. SOLUTION: Subtract each term from the term directly after it. 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. The common difference is 7. Therefore, the sequence is arithmetic. ANSWER: The common difference is 12. Yes Therefore, the sequence is arithmetic. To find the next term, add 12 to the last term. 3. 1, 2, 4, 8, 16 30 + 12 = 42 42 + 12 = 54 SOLUTION: 54 + 12 = 66 66 + 12 = 78 Subtract each term from the term directly after it. Graph the sequence. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No 4. 0.6, 0.9, 1.2, 1.8, ... ANSWER: 42, 54, 66, 78 SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No 6. 15, 6, –3, … Find the next four terms of each arithmetic sequence. Then graph the sequence. SOLUTION: Subtract each term from the term directly after it. 5. 6, 18, 30, … SOLUTION: Subtract each term from the term directly after it. The common difference is –9. Therefore, the sequence is arithmetic. To find the next term, add –9 to the last term. The common difference is 12. –3 + (–9) = –12 Therefore, the sequence is arithmetic. –12 + (–9) = –21 –21 + (–9) = –30 To find the next term, add 12 to the last term. –30 + (–9) = –39 30 + 12 = 42 42 + 12 = 54 Graph the sequence. 54 + 12 = 66 66 + 12 = 78 Graph the sequence. ANSWER: –12, –21, –30, –39 ANSWER: 42, 54, 66, 78 7. –19, –11, –3, … SOLUTION: Subtract each term from the term directly after it. 6. 15, 6, –3, … SOLUTION: The common difference is 8. Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the next term, add 8 to the last term. –3 + 8 = 5 5 + 8 = 13 The common difference is –9. 13 + 8 = 21 Therefore, the sequence is arithmetic. 21 + 8 = 29 To find the next term, add –9 to the last term. Graph the sequence. –3 + (–9) = –12 –12 + (–9) = –21 –21 + (–9) = –30 –30 + (–9) = –39 Graph the sequence. ANSWER: 5, 13, 21, 29 ANSWER: –12, –21, –30, –39 8. –26, –33, –40, … SOLUTION: Subtract each term from the term directly after it. 7. –19, –11, –3, … SOLUTION: The common difference is –7. Subtract each term from the term directly after it. Therefore, the sequence is arithmetic. To find the next term, add –7 to the last term. –40 + (–7) = –47 The common difference is 8. –47 + (–7) = –54 Therefore, the sequence is arithmetic. –54 + (–7) = –61 –61 + (–7) = –68 To find the next term, add 8 to the last term. Graph the sequence. –3 + 8 = 5 5 + 8 = 13 13 + 8 = 21 21 + 8 = 29 Graph the sequence. ANSWER: –47, –54, –61, –68 ANSWER: 5, 13, 21, 29 9. FINANCIAL LITERACY Kelly is saving her money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. a. How much will Kelly have saved after 8 weeks? 8. –26, –33, –40, … b. If the car costs $2000, how long will it take her to save enough money at this rate? SOLUTION: Subtract each term from the term directly after it. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. b. Given a = 2000. The common difference is –7. n Therefore, the sequence is arithmetic. Find n. To find the next term, add –7 to the last term. –40 + (–7) = –47 –47 + (–7) = –54 –54 + (–7) = –61 –61 + (–7) = –68 So, it will take about 24 weeks to save $2000. Graph the sequence. ANSWER: a. $850 b. 24 wk Determine whether each sequence is geometric. Write yes or no. 10. –8, –5, –1, 4, … ANSWER: –47, –54, –61, –68 SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: 9. FINANCIAL LITERACY Kelly is saving her No money to buy a car. She has $250, and she plans to save $75 per week from her job as a waitress. 11. 4, 12, 36, 108, … a. How much will Kelly have saved after 8 weeks? b. If the car costs $2000, how long will it take her to SOLUTION: save enough money at this rate? Find the ratio of the consecutive terms. SOLUTION: a. Given a = 250, d = 75 and n = 8. 0 After 8 weeks, she will have 250 + (8 × 75) or $850. Since the ratios are the same, the sequence is geometric. b. Given a = 2000. n ANSWER: Find n. Yes 12. 27, 9, 3, 1, … SOLUTION: So, it will take about 24 weeks to save $2000. Find the ratio of the consecutive terms. ANSWER: a. $850 Since the ratios are the same, the sequence is b. 24 wk geometric. Determine whether each sequence is ANSWER: geometric. Write yes or no. Yes 10. –8, –5, –1, 4, … 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. Since the ratios are not the same, the sequence is not geometric. ANSWER: No ANSWER: No 11. 4, 12, 36, 108, … Find the next three terms of each geometric sequence. Then graph the sequence. SOLUTION: Find the ratio of the consecutive terms. 14. 8, 12, 18, 27, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. ANSWER: Since the ratios are the same, the sequence is geometric Yes To find the next term, multiply the previous term by 12. 27, 9, 3, 1, … . SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric. Graph the sequence. ANSWER: Yes 13. 7, 14, 21, 28, … SOLUTION: Find the ratio of the consecutive terms. ANSWER: 40.5, 60.75, 91.125 Since the ratios are not the same, the sequence is not geometric. ANSWER: No Find the next three terms of each geometric sequence. Then graph the sequence. 14. 8, 12, 18, 27, … 15. 8, 16, 32, 64, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric Since the ratios are the same, the sequence is To find the next term, multiply the previous term by geometric. . To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 40.5, 60.75, 91.125 16. 250, 50, 10, 2, … SOLUTION: 15. 8, 16, 32, 64, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are the same, the sequence is geometric To find the next term, multiply the previous term by Since the ratios are the same, the sequence is geometric. . To find the next term, multiply the previous term by 2. Graph the sequence. Graph the sequence. ANSWER: 128, 256, 512 ANSWER: 16. 250, 50, 10, 2, … SOLUTION: Find the ratio of the consecutive terms. 17. 9, –3, 1, , … SOLUTION: Since the ratios are the same, the sequence is Find the ratio of the consecutive terms. geometric To find the next term, multiply the previous term by . Since the ratios are the same, the sequence is geometric. To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 17. 9, –3, 1, , … SOLUTION: Find the ratio of the consecutive terms. Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 18. 5, 1, 7, 3, 9, … Since the ratios are the same, the sequence is geometric. SOLUTION: To find the next term, multiply the previous term by . There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Graph the sequence. ANSWER: Neither; there is no common difference or ratio. 19. 200, –100, 50, –25, … SOLUTION: To find the common difference, subtract any term from the term directly after it. ANSWER: There is no common difference. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. The common ratio is . Since the ratios are the same, the sequence is Determine whether each sequence is geometric. arithmetic, geometric, or neither. Explain your reasoning. ANSWER: 18. 5, 1, 7, 3, 9, … Geometric; the common ratio is . SOLUTION: 20. 12, 16, 20, 24, … SOLUTION: There is no common difference. To find the common difference, subtract any term Therefore, the sequence is not arithmetic. from the term directly after it. Find the ratio of the consecutive terms. The common difference is 4. Since the ratios are not the same, the sequence is not Therefore, the sequence is arithmetic. geometric. Find the ratio of the consecutive terms. ANSWER: Neither; there is no common difference or ratio. Since the ratios are not the same, the sequence is not 19. 200, –100, 50, –25, … geometric. SOLUTION: ANSWER: To find the common difference, subtract any term Arithmetic; the common difference is 4. from the term directly after it. Determine whether each sequence is arithmetic. Write yes or no. There is no common difference. 21. Therefore, the sequence is not arithmetic. Find the ratio of the consecutive terms. SOLUTION: Subtract any term from the term directly after it. The common ratio is . Since the ratios are the same, the sequence is geometric. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: ANSWER: Geometric; the common ratio is . No 20. 12, 16, 20, 24, … 22. –9, –3, 0, 3, 9 SOLUTION: SOLUTION: To find the common difference, subtract any term Subtract any term from the term directly after it. from the term directly after it. There is no common difference. The common difference is 4. Therefore, the sequence is not arithmetic. Therefore, the sequence is arithmetic. Find the ratio of the consecutive terms. ANSWER: No 23. 14, –5, –19, … Since the ratios are not the same, the sequence is not geometric. SOLUTION: Subtract any term from the term directly after it. ANSWER: Arithmetic; the common difference is 4. Determine whether each sequence is There is no common difference. arithmetic. Write yes or no. Therefore, the sequence is not arithmetic. 21. ANSWER: No SOLUTION: Subtract any term from the term directly after it. 24. SOLUTION: Subtract any term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: No The common difference is . Therefore, the sequence is arithmetic. 22. –9, –3, 0, 3, 9 ANSWER: SOLUTION: Yes Subtract any term from the term directly after it. Find the next four terms of each arithmetic sequence. Then graph the sequence. 25. –4, –1, 2, 5,… There is no common difference. Therefore, the sequence is not arithmetic. SOLUTION: Subtract any term from the term directly after it. ANSWER: No 23. 14, –5, –19, … The common difference is 3. Therefore, the sequence is arithmetic. SOLUTION: Subtract any term from the term directly after it. To find the next term, add 3 to the last term. 5 + 3 = 8 8 + 3 = 11 11 + 3 = 14 There is no common difference. 14 + 3 = 17 Therefore, the sequence is not arithmetic. Graph the sequence. ANSWER: No 24. SOLUTION: Subtract any term from the term directly after it. ANSWER: 8, 11, 14, 17 The common difference is . Therefore, the sequence is arithmetic. ANSWER: 10-1Y Seesq uences as Functions Find the next four terms of each arithmetic 26. 10, 2, –6, –14, … sequence. Then graph the sequence. SOLUTION: 25. –4, –1, 2, 5,… Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is –8. Therefore, this sequence is arithmetic. The common difference is 3. To find the next term, add –8 to the last term. Therefore, the sequence is arithmetic. –14 + (–8) = –22 To find the next term, add 3 to the last term. –22 + (–8) = –30 –30 + (–8) = –38 5 + 3 = 8 –38 + (–8) = –46 8 + 3 = 11 11 + 3 = 14 Graph the sequence. 14 + 3 = 17 Graph the sequence. ANSWER: –22, –30, –38, – 46 ANSWER: 8, 11, 14, 17 27. –5, –11, –17, –23, … SOLUTION: 26. 10, 2, –6, –14, … Subtract any term from the term directly after it. eSolut i onsManual-PoweredbyCognero Page10 SOLUTION: Subtract any term from the term directly after it. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add –6 to the last term. The common difference is –8. Therefore, this sequence is arithmetic. –23 + (–6) = –29 –29 + (–6) = –35 To find the next term, add –8 to the last term. –35 + (–6) = –41 –41 + (–6) = –47 –14 + (–8) = –22 –22 + (–8) = –30 Graph the sequence. –30 + (–8) = –38 –38 + (–8) = –46 Graph the sequence. ANSWER: –29, –35, – 41, – 47 ANSWER: –22, –30, –38, – 46 28. –19, –2, 15, … 27. –5, –11, –17, –23, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. Therefore, the sequence is arithmetic. The common difference is –6. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. To find the next term, add –6 to the last term. 15 + 17 = 32 32 + 17 = 49 –23 + (–6) = –29 49 + 17 = 66 –29 + (–6) = –35 66 + 17 = 83 –35 + (–6) = –41 –41 + (–6) = –47 Graph the sequence. Graph the sequence. ANSWER: 32, 49, 66, 83 ANSWER: –29, –35, – 41, – 47 29. 28. –19, –2, 15, … SOLUTION: Subtract any term from the term directly after it. SOLUTION: Subtract any term from the term directly after it. The common difference is 17. The common difference is . Therefore, the sequence is arithmetic. Therefore, the sequence is arithmetic. To find the next term, add 17 to the last term. 15 + 17 = 32 To find the next term, add to the last term. 32 + 17 = 49 49 + 17 = 66 66 + 17 = 83 Graph the sequence. Graph the sequence. ANSWER: 32, 49, 66, 83 ANSWER: 29. SOLUTION: Subtract any term from the term directly after it. 30. SOLUTION: The common difference is . Subtract any term from the term directly after it. Therefore, the sequence is arithmetic. To find the next term, add to the last term. The common difference is –1. Therefore, the sequence is arithmetic. To find the next term, add −1 to the last term. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 30. SOLUTION: Subtract any term from the term directly after it. 31. THEATER There are 28 seats in the front row of a theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: The common difference is –1. Given a = 28, d = 2 and n = 24. Therefore, the sequence is arithmetic. 1 To find the next term, add −1 to the last term. Find a . 24 ANSWER: 74 Graph the sequence. 32. CCSS SENSE-MAKING Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. a. How long will he row on the 18th day? b. On what day will Mario first row an hour or more? c. Is it reasonable for this pattern to continue indefinitely? Explain. ANSWER: SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Find a . 18 Therefore he will row for 30 minutes and 30 seconds on the 38th day. b. Given a = 5, d = 1.5 and a = 60. 31. THEATER There are 28 seats in the front row of a 1 n Find n. theater. Each successive row contains two more seats than the previous row. If there are 24 rows, how many seats are in the last row of the theater? SOLUTION: Given a = 28, d = 2 and n = 24. 1 Mario will first row an hour or more on the 38th day. Find a . 24 c. Sample answer: It is unreasonable because there are only so many hours in the day that can be dedicated to rowing. ANSWER: a. 30 minutes and 30 seconds ANSWER: b. on the 38th day 74 c. Sample answer: It is unreasonable because there 32. CCSS SENSE-MAKING Mario began an exercise are only so many hours in the day that can be program to get back in shape. He plans to row 5 dedicated to rowing. minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day. Determine whether each sequence is geometric. Write yes or no. a. How long will he row on the 18th day? 33. 21, 14, 7, … b. On what day will Mario first row an hour or more? SOLUTION: c. Is it reasonable for this pattern to continue Find the ratio of the consecutive terms. indefinitely? Explain. SOLUTION: a. Given a = 5, d = 1.5 and n = 18. 1 Since the ratios are not the same, the sequence is not geometric. Find a . 18 ANSWER: No Therefore he will row for 30 minutes and 30 seconds 34. 124, 186, 248, … on the 38th day. b. Given a = 5, d = 1.5 and a = 60. SOLUTION: 1 n Find n. Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Mario will first row an hour or more on the 38th day. ANSWER: c. Sample answer: It is unreasonable because there No are only so many hours in the day that can be dedicated to rowing. 35. –27, 18, –12, … ANSWER: SOLUTION: a. 30 minutes and 30 seconds Find the ratio of the consecutive terms. b. on the 38th day Since the ratios are the same, the sequence is c. Sample answer: It is unreasonable because there geometric. are only so many hours in the day that can be dedicated to rowing. ANSWER: Yes Determine whether each sequence is 36. 162, 108, 72, … geometric. Write yes or no. SOLUTION: 33. 21, 14, 7, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. ANSWER: Yes Since the ratios are not the same, the sequence is not geometric. 37. ANSWER: No SOLUTION: Find the ratio of the consecutive terms. 34. 124, 186, 248, … SOLUTION: Find the ratio of the consecutive terms. Since the ratios are not the same, the sequence is not geometric. Since the ratios are not same, the sequence is not ANSWER: geometric. No ANSWER: 35. –27, 18, –12, … No SOLUTION: Find the ratio of the consecutive terms. 38. –4, –2, 0, 2, … Since the ratios are the same, the sequence is SOLUTION: geometric. Find the ratio of the consecutive terms. ANSWER: Yes 36. 162, 108, 72, … Since the ratios are not same, the sequence is not geometric. SOLUTION: Find the ratio of the consecutive terms. ANSWER: No Find the next three terms of the sequence. Since the ratios are same, the sequence is geometric. Then graph the sequence. 39. 0.125, –0.5, 2, … ANSWER: Yes SOLUTION: Find the ratio of the consecutive terms. 37. SOLUTION: Since the ratios are same, the sequence is geometric Find the ratio of the consecutive terms. To find the next term, multiply the previous term with −4. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: No 38. –4, –2, 0, 2, … ANSWER: SOLUTION: – 8, 32, –128 Find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. ANSWER: No Find the next three terms of the sequence. 40. 18, 12, 8, … Then graph the sequence. 39. 0.125, –0.5, 2, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric . To find the next term, multiply the previous term with −4. Graph the sequence. Graph the sequence. ANSWER: – 8, 32, –128 ANSWER: 40. 18, 12, 8, … SOLUTION: 41. 64, 48, 36, … Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric. . To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 41. 64, 48, 36, … 42. 81, 108, 144, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric . To find the next term, multiply the previous term by . Graph the sequence. Graph the sequence. ANSWER: ANSWER: 42. 81, 108, 144, … 43. SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by . Since the ratios are same, the sequence is geometric To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: ANSWER: 27, 81, 243 44. 1, 0.1, 0.01, 0.001, … 43. SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Find the ratio of the consecutive terms. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by Since the ratios are same, the sequence is geometric 0.1. To find the next term, multiply the previous term by 3. Graph the sequence. Graph the sequence. ANSWER: 0.0001, 0.00001, 0.000001 ANSWER: 27, 81, 243 Determine whether each sequence is arithmetic, geometric, or neither. Explain your reasoning. 44. 1, 0.1, 0.01, 0.001, … 45. 3, 12, 27, 48, … SOLUTION: Find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are same, the sequence is geometric. To find the next term, multiply the previous term by There is no common difference. 0.1. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Graph the sequence. Since the ratios are not same, the sequence is not geometric. ANSWER: Neither; there is no common difference or ratio. 46. 1, –2, –5, –8, … ANSWER: SOLUTION: 0.0001, 0.00001, 0.000001 Subtract each term from the term directly after it. The common difference is –3. Therefore, the sequence is arithmetic. To find the common ratio, find the ratio of the consecutive terms. Determine whether each sequence is arithmetic, geometric, or neither. Explain your Since the ratios are not same, the sequence is not geometric. reasoning. 45. 3, 12, 27, 48, … ANSWER: Arithmetic; the common difference is –3. SOLUTION: Subtract each term from the term directly after it. 47. 12, 36, 108, 324, … SOLUTION: Subtract each term from the term directly after it. There is no common difference. Therefore, the sequence is not arithmetic. To find the common ratio, find the ratio of the There is no common difference. consecutive terms. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. Since the ratios are not same, the sequence is not geometric. The common ratio is 3. ANSWER: Neither; there is no common difference or ratio. Since the ratios are same, the sequence is geometric. 46. 1, –2, –5, –8, … ANSWER: Geometric; the common ratio is 3. SOLUTION: Subtract each term from the term directly after it. 48. SOLUTION: The common difference is –3. Therefore, the sequence is arithmetic. Subtract each term from the term directly after it. To find the common ratio, find the ratio of the consecutive terms. There is no common difference. Therefore, this sequence is not arithmetic. Since the ratios are not same, the sequence is not geometric. To find the common ratio, find the ratio of the consecutive terms. ANSWER: Arithmetic; the common difference is –3. 47. 12, 36, 108, 324, … The common ratio is . SOLUTION: Since the ratios are the same, the sequence is Subtract each term from the term directly after it. geometric. ANSWER: Geometric; the common ratio is . There is no common difference. Therefore, this sequence is not arithmetic. To find the common ratio, find the ratio of the consecutive terms. 49. SOLUTION: Subtract each term from the term directly after it. The common ratio is 3. Since the ratios are same, the sequence is geometric. ANSWER: Geometric; the common ratio is 3. The common difference is . Therefore, the sequence is arithmetic. 48. To find the common ratio, find the ratio of the consecutive terms. SOLUTION: Subtract each term from the term directly after it. Since the ratios are not same, the sequence is not geometric. There is no common difference. ANSWER: Therefore, this sequence is not arithmetic. Arithmetic; the common difference is . To find the common ratio, find the ratio of the consecutive terms. 50. 6, 9, 14, 21, … SOLUTION: Subtract each term from the term directly after it. The common ratio is . Since the ratios are the same, the sequence is geometric. There is no common difference. Therefore, the sequence is not arithmetic. ANSWER: To find the common ratio, find the ratio of the Geometric; the common ratio is . consecutive terms. 49. Since the ratios are not same, the sequence is not geometric. SOLUTION: Subtract each term from the term directly after it. ANSWER: Neither; there is no common difference or ratio. 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day The common difference is . to finish the book by the end of her vacation? Therefore, the sequence is arithmetic. SOLUTION: To find the common ratio, find the ratio of the The number of pages to be read is 800 – 112 or 688. consecutive terms. The minimum number of pages to read per day is . Since the ratios are not same, the sequence is not geometric. ANSWER: 86 pg/day ANSWER: Arithmetic; the common difference is . 52. DEPRECIATION Tammy’s car is expected to depreciate at a rate of 15% per year. If her car is currently valued at $24,000, to the nearest dollar, how much will it be worth in 6 years? 50. 6, 9, 14, 21, … SOLUTION: SOLUTION: Substitute 0.15, 6 and 24000 for r, t and P in Subtract each term from the term directly after it. then evaluate. There is no common difference. Therefore, the sequence is not arithmetic. The worth of the car will be about $9052 after 6 years. To find the common ratio, find the ratio of the consecutive terms. ANSWER: $9052 53. CCSS REGULARITY When a piece of paper is Since the ratios are not same, the sequence is not folded onto itself, it doubles in thickness. If a piece of geometric. paper that is 0.1 mm thick could be folded 37 times, how thick would it be? ANSWER: Neither; there is no common difference or ratio. SOLUTION: Given a = 0.1, n = 37 and r = 2. 0 51. READING Sareeta took an 800-page book on vacation. If she was already on page 112 and is Find a . 37 going to be on vacation for 8 days, what is the minimum number of pages she needs to read per day to finish the book by the end of her vacation? SOLUTION: The number of pages to be read is 800 – 112 or 688. The thickness would be about 13,744 km. The minimum number of pages to read per day is . ANSWER: about 13,744 km ANSWER: 54. REASONING Explain why the sequence 8, 10, 13, 86 pg/day 17, 22 is not arithmetic. SOLUTION: 52. DEPRECIATION Tammy’s car is expected to Sample answer: The consecutive terms do not share depreciate at a rate of 15% per year. If her car is a common difference. For instance, 22 – 17 = 5, currently valued at $24,000, to the nearest dollar, while 17 – 13 = 4. how much will it be worth in 6 years? SOLUTION: ANSWER: Substitute 0.15, 6 and 24000 for r, t and P in Sample answer: The consecutive terms do not share a common difference. For instance, 22 – 17 = 5, then evaluate. while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. The worth of the car will be about $9052 after 6 years. SOLUTION: Sample answer: A babysitter earns $20 for cleaning ANSWER: the house and $8 extra for every hour she watches $9052 the children. 53. CCSS REGULARITY When a piece of paper is ANSWER: folded onto itself, it doubles in thickness. If a piece of Sample answer: A babysitter earns $20 for cleaning paper that is 0.1 mm thick could be folded 37 times, the house and $8 extra for every hour she watches how thick would it be? the children. SOLUTION: 56. CHALLENGE The sum of three consecutive terms Given a = 0.1, n = 37 and r = 2. of an arithmetic sequence is 6. The product of the 0 terms is –42. Find the terms. Find a . SOLUTION: 37 Let x be the first term in the arithmetic sequence. Therefore, the next two terms should be x + d and x + 2d. The thickness would be about 13,744 km. ANSWER: about 13,744 km 54. REASONING Explain why the sequence 8, 10, 13, 17, 22 is not arithmetic. Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. SOLUTION: Sample answer: The consecutive terms do not share ANSWER: a common difference. For instance, 22 – 17 = 5, –3, 2, 7 while 17 – 13 = 4. 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is ANSWER: arithmetic, geometric, neither, or both. Is either of Sample answer: The consecutive terms do not share them correct? Explain your reasoning. a common difference. For instance, 22 – 17 = 5, while 17 – 13 = 4. 55. OPEN ENDED Describe a real-life situation that can be represented by an arithmetic sequence with a common difference of 8. SOLUTION: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches the children. ANSWER: Sample answer: A babysitter earns $20 for cleaning the house and $8 extra for every hour she watches SOLUTION: the children. Sample answer: Neither; the sequence is both arithmetic and geometric. 56. CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6. The product of the terms is –42. Find the terms. ANSWER: SOLUTION: Sample answer: Neither; the sequence is both Let x be the first term in the arithmetic sequence. arithmetic and geometric. Therefore, the next two terms should be x + d and x + 2d. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… . Sample answer: Let d = 5. Therefore, the terms are –3, 2, 7. ANSWER: –3, 2, 7 57. ERROR ANALYSIS Brody and Gen are determining whether the sequence 8, 8, 8,… is arithmetic, geometric, neither, or both. Is either of them correct? Explain your reasoning. SOLUTION: Sample answer: Neither; the sequence is both arithmetic and geometric. ANSWER: Sample answer: Neither; the sequence is both arithmetic and geometric. 58. OPEN ENDED Find a geometric sequence, an arithmetic sequence, and a sequence that is neither geometric nor arithmetic that begins 3, 9,… .

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Therefore, the sequence is not arithmetic. ANSWER: .. READING Sareeta took an 800-page book on to finish the book by the end of her vacation?

Determine whether each sequence is arithmetic no. 1. 8 PDF

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Therefore, the sequence is not arithmetic. ANSWER: .. READING Sareeta took an 800-page book on to finish the book by the end of her vacation?

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