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Arithmetic Sequences Math34: Spring2015 Arithmetic Sequences Arithmetic Sequences Supplemental Material Not Found in You Text Review RealWorld Examples GeneralWay Math 34: Spring 2015 toWritean Arithmetic Sequence Formula Examples DoNOTprinttheseslides!! PartialSums Formula Examples Thereareprinterfriendlyfilesonthewebsite. Homework January 28, 2015 Arithmetic Sequences Arithmetic Sequences Math34: 1 Arithmetic Sequences Spring2015 Review Arithmetic Real World Examples Sequences Review RealWorld 2 General Way to Write an Arithmetic Sequence Examples GeneralWay Formula toWritean Arithmetic Examples Sequence Formula Examples 3 Partial Sums PartialSums Formula Formula Examples Examples Homework 4 Homework IS arithmetic, with constant difference d =3 is NOT arithmetic IS arithmetic, with constant difference d =10 1 1,4,7,10,13,... 2 2,4,8,16,32,... 3 −3,7,17,27,... Which of the following are Arithmetic Sequences? Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Formula Examples PartialSums Formula Examples Homework IS arithmetic, with constant difference d =3 is NOT arithmetic IS arithmetic, with constant difference d =10 Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Which of the following are Arithmetic Sequences? Formula Examples 1 1,4,7,10,13,... PartialSums Formula 2 2,4,8,16,32,... Examples Homework 3 −3,7,17,27,... is NOT arithmetic IS arithmetic, with constant difference d =10 Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Which of the following are Arithmetic Sequences? Formula Examples 1 1,4,7,10,13,... PartialSums IS arithmetic, with constant difference d =3 Formula 2 2,4,8,16,32,... Examples Homework 3 −3,7,17,27,... IS arithmetic, with constant difference d =10 Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Which of the following are Arithmetic Sequences? Formula Examples 1 1,4,7,10,13,... PartialSums IS arithmetic, with constant difference d =3 Formula 2 2,4,8,16,32,... Examples is NOT arithmetic Homework 3 −3,7,17,27,... Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Which of the following are Arithmetic Sequences? Formula Examples 1 1,4,7,10,13,... PartialSums IS arithmetic, with constant difference d =3 Formula 2 2,4,8,16,32,... Examples is NOT arithmetic Homework 3 −3,7,17,27,... IS arithmetic, with constant difference d =10 Both these scenarios can be modeled by Arithmetic Sequences, and we will develop tools to help us answer these questions. Real World Examples Arithmetic Sequences 1 You start a new job and you’re told you salary is $29,000 Math34: for the first year, and that you’ll get a $1700 raise each Spring2015 year. What will your salary be in the third year? What will Arithmetic Sequences your salary be in 10 years? How long does it take for your Review salary to (at least) double? RealWorld Examples GeneralWay toWritean Arithmetic 2 A new company has a loss of $2,500 in its first month, Sequence but they expect their monthly profit to increase by $400 Formula Examples each month. What is their profit in the 12th month? PartialSums What is their total profit/loss of the year? Formula Examples Homework Real World Examples Arithmetic Sequences 1 You start a new job and you’re told you salary is $29,000 Math34: for the first year, and that you’ll get a $1700 raise each Spring2015 year. What will your salary be in the third year? What will Arithmetic Sequences your salary be in 10 years? How long does it take for your Review salary to (at least) double? RealWorld Examples GeneralWay toWritean Arithmetic 2 A new company has a loss of $2,500 in its first month, Sequence but they expect their monthly profit to increase by $400 Formula Examples each month. What is their profit in the 12th month? PartialSums What is their total profit/loss of the year? Formula Examples Homework Both these scenarios can be modeled by Arithmetic Sequences, and we will develop tools to help us answer these questions. Look at the pattern that the common difference of 2 creates. 5, 7, 9, 11, 13, ... 5 , 5+(1)2, 5+(2)2, 5+(3)2, 5+(4)2, ... (cid:124)(cid:123)(cid:122)(cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) a1 a2 a3 a4 a5 We notice the pattern for this sequence a = 5+(n−1)2 n We also see that a = a +2 (each term is 2 more than the n n−1 previous term) General Way to Write an Arithmetic Sequence Arithmetic Sequences Math34: Consider the Arithmetic Sequence below. Notice the first Spring2015 term is 5 and the common difference is 2: Arithmetic Sequences Review 5,7,9,11,13,... RealWorld Examples GeneralWay toWritean Arithmetic Sequence Formula Examples PartialSums Formula Examples Homework

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Arithmetic Sequences Math 34: Spring 2015 Arithmetic Sequences Review Real World Examples General Way to Write an Arithmetic Sequence Formula Examples Partial Sums
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Arithmetic Sequences Math34: Spring2015 Arithmetic Sequences Arithmetic Sequences Supplemental Material Not Found in You Text Review RealWorld Examples GeneralWay Math 34: Spring 2015 toWritean Arithmetic Sequence Formula Examples DoNOTprinttheseslides!! PartialSums Formula Examples Thereareprinterfriendlyfilesonthewebsite. Homework January 28, 2015 Arithmetic Sequences Arithmetic Sequences Math34: 1 Arithmetic Sequences Spring2015 Review Arithmetic Real World Examples Sequences Review RealWorld 2 General Way to Write an Arithmetic Sequence Examples GeneralWay Formula toWritean Arithmetic Examples Sequence Formula Examples 3 Partial Sums PartialSums Formula Formula Examples Examples Homework 4 Homework IS arithmetic, with constant difference d =3 is NOT arithmetic IS arithmetic, with constant difference d =10 1 1,4,7,10,13,... 2 2,4,8,16,32,... 3 −3,7,17,27,... Which of the following are Arithmetic Sequences? Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Formula Examples PartialSums Formula Examples Homework IS arithmetic, with constant difference d =3 is NOT arithmetic IS arithmetic, with constant difference d =10 Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Which of the following are Arithmetic Sequences? Formula Examples 1 1,4,7,10,13,... PartialSums Formula 2 2,4,8,16,32,... Examples Homework 3 −3,7,17,27,... is NOT arithmetic IS arithmetic, with constant difference d =10 Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Which of the following are Arithmetic Sequences? Formula Examples 1 1,4,7,10,13,... PartialSums IS arithmetic, with constant difference d =3 Formula 2 2,4,8,16,32,... Examples Homework 3 −3,7,17,27,... IS arithmetic, with constant difference d =10 Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Which of the following are Arithmetic Sequences? Formula Examples 1 1,4,7,10,13,... PartialSums IS arithmetic, with constant difference d =3 Formula 2 2,4,8,16,32,... Examples is NOT arithmetic Homework 3 −3,7,17,27,... Arithmetic Sequences Arithmetic Sequences Math34: Recall an Arithmetic Sequence is a sequence where the Spring2015 difference between any two consecutive numbers in the Arithmetic sequence is constant. Sequences Review RExeaamlWploersld In other words: ak+1−ak = d where d is a constant. GeneralWay toWritean Arithmetic Sequence Which of the following are Arithmetic Sequences? Formula Examples 1 1,4,7,10,13,... PartialSums IS arithmetic, with constant difference d =3 Formula 2 2,4,8,16,32,... Examples is NOT arithmetic Homework 3 −3,7,17,27,... IS arithmetic, with constant difference d =10 Both these scenarios can be modeled by Arithmetic Sequences, and we will develop tools to help us answer these questions. Real World Examples Arithmetic Sequences 1 You start a new job and you’re told you salary is $29,000 Math34: for the first year, and that you’ll get a $1700 raise each Spring2015 year. What will your salary be in the third year? What will Arithmetic Sequences your salary be in 10 years? How long does it take for your Review salary to (at least) double? RealWorld Examples GeneralWay toWritean Arithmetic 2 A new company has a loss of $2,500 in its first month, Sequence but they expect their monthly profit to increase by $400 Formula Examples each month. What is their profit in the 12th month? PartialSums What is their total profit/loss of the year? Formula Examples Homework Real World Examples Arithmetic Sequences 1 You start a new job and you’re told you salary is $29,000 Math34: for the first year, and that you’ll get a $1700 raise each Spring2015 year. What will your salary be in the third year? What will Arithmetic Sequences your salary be in 10 years? How long does it take for your Review salary to (at least) double? RealWorld Examples GeneralWay toWritean Arithmetic 2 A new company has a loss of $2,500 in its first month, Sequence but they expect their monthly profit to increase by $400 Formula Examples each month. What is their profit in the 12th month? PartialSums What is their total profit/loss of the year? Formula Examples Homework Both these scenarios can be modeled by Arithmetic Sequences, and we will develop tools to help us answer these questions. Look at the pattern that the common difference of 2 creates. 5, 7, 9, 11, 13, ... 5 , 5+(1)2, 5+(2)2, 5+(3)2, 5+(4)2, ... (cid:124)(cid:123)(cid:122)(cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) a1 a2 a3 a4 a5 We notice the pattern for this sequence a = 5+(n−1)2 n We also see that a = a +2 (each term is 2 more than the n n−1 previous term) General Way to Write an Arithmetic Sequence Arithmetic Sequences Math34: Consider the Arithmetic Sequence below. Notice the first Spring2015 term is 5 and the common difference is 2: Arithmetic Sequences Review 5,7,9,11,13,... RealWorld Examples GeneralWay toWritean Arithmetic Sequence Formula Examples PartialSums Formula Examples Homework

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