Table Of Content1
Secondary Mathematics I:
An Integrated Approach
Module 3
Arithmetic and Geometric
Sequences
By
The Mathematics Vision Project:
Scott Hendrickson, Joleigh Honey,
Barbara Kuehl, Travis Lemon, Janet Sutorius
www.mathematicsvisionproject.org
In partnership with the
Utah State Office of Education
V
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.
Sequences 1
Math 1: Intro to Arithmetic Sequences Name:_____________________________
Pd:_____
Congratulations, you have just won The Fillmore High School lottery! You are given the option of receiving your
payments in one of two ways for the next 16 days:
Would you rather
Receive $20 a day for 16 days
Or
For the next 16 days, double 1 penny on Day 1 for a total of 2 pennies and receive 2 more pennies on Day 2, 4 more
pennies on Day 3, 8 more on Day 4, etc.?
1.) Which payment would you choose? Why?
2.) How much money would each one give you after 5 days?
$20 a day (start with 0) Pennies a day (start with 1)
Day $ added Total $ Day $ added Total $
1 20 20 1 .01 .02
2 20 40 2 .02 .04
3 20 60 3 .04 .08
4 20 80 4 .08 .16
5 5
3.) How much money after 10 days? 15 days?
4.) If the contest went for 16 days, which option would you choose? How much money would you make? Check the
other option at 16 days. Did you make a good choice? Why?
5.) Plot your point (Days, $ Total) on the graph.
DAYS
6) Look at the $20 a day, what is the amount changing by each day? (i.e., what is the slope?)
7) Look at the pennies a day, what happens to the amount each day?
8) Try to create an equation for the $20 a day. (hint: it is a line)
9) Try to create an equation for the pennies a day. (hint: it doubles each time, 2 * 2 * 2 * …* 2)
10) What would the difference in the total dollars between the two be after 20 days?
Bonus:
Each $20 dollar bill weighs .002 lbs. What would the weight be of your $20 dollar bills be after 15 days of receiving
them?
Each penny weighs .006 lbs. What would the weight be of your pennies after 15 days of receiving them?
Homework Math 1: Introduction to Arithmetic and Geometric Sequence
3
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mit
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c
3.1Growing Dots de
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o
A Develop Understanding Task hot
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2
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1. Describe the pattern that you see in the sequence of figures above.
2. Assuming the sequence continues in the same way, how many dots are there at 3
minutes?
3. How many dots are there at 100 minutes?
4. How many dots are there at t minutes?
Solve the problems by your preferred method. Your solution should indicate how many
dots will be in the pattern at 3 minutes, 100 minutes, and t minutes. Be sure to show how
your solution relates to the picture and how you arrived at your solution.
V
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.
Sequences 3
4
Name:
Sequences
3.1
Ready,
Set,
Go!
©
2012
www.flickr.com/photos/fdecomite
Ready
Topic:
Exponents,
Substitution,
and
Function
Notation
Find
each
value.
1. 3!
2.
3!
3.
3!
4.
3!
For
each
of
the
following,
find
f
(1),
f
(2)
and
f
(3)
5. 𝑓 𝑥 = 2!
6.
𝑓 𝑥 = 3!
7.
𝑓 𝑥 = 2 𝑥−1 +3
Complete
each
table.
8.
Term
1st
2nd
3rd
4th
5th
6th
7th
8th
Value
2
4
8
16
32
9.
Term
1st
2nd
3rd
4th
5th
6th
7th
8th
Value
66
50
34
18
10.
Term
1st
2nd
3rd
4th
5th
6th
7th
8th
Value
-‐3
9
-‐27
81
11.
Term
1st
2nd
3rd
4th
5th
6th
7th
8th
Value
160
80
40
20
12.
Term
1st
2nd
3rd
4th
5th
6th
7th
8th
Value
-‐9
-‐2
5
12
V
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed
under
the
Creative
Commons
Attribution-‐NonCommercial-‐ShareAlike
3.0
Unported
license
Sequences 4
5
Name:
Sequences
3.1
Set
Topic:
Completing
a
table
Fill
in
the
table.
Then
write
a
sentence
explaining
how
you
figured
out
the
values
to
put
in
each
cell.
Explain
how
to
figure
out
what
will
be
in
cell
#8.
13. You
run
a
business
making
birdhouses.
You
spend
$600
to
start
your
business,
and
it
costs
you
$5.00
to
make
each
birdhouse.
#
of
birdhouses
1
2
3
4
5
6
7
Total
cost
to
build
Explanation:
14. You
borrow
$500
from
a
relative,
and
you
agree
to
pay
back
the
debt
at
a
rate
of
$15
per
month.
#
of
months
1
2
3
4
5
6
7
Amount
of
money
owed
Explanation:
15. You
earn
$10
per
week.
#
of
weeks
1
2
3
4
5
6
7
Amount
of
money
earned
Explanation:
16. You
are
saving
for
a
bike
and
can
save
$10
per
week.
You
have
$25
already
saved.
#
of
weeks
1
2
3
4
5
6
7
Amount
of
money
saved
Explanation:
V
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed
under
the
Creative
Commons
Attribution-‐NonCommercial-‐ShareAlike
3.0
Unported
license
Sequences 5
6
Name:
Sequences
3.1
Go
Topic:
Good
viewing
window
1
When
sketching
a
graph
of
a
Example:
g
(x)
=
x
–
6
function,
it
is
important
that
3
we
see
important
points.
For
Window:
[
-‐10,
10]
by
[
-‐10,10]
Window:
[-‐10,
25]
by
[
-‐10,
5]
linear
functions,
we
want
a
x-‐
scale:
1
y-‐scale:
1
x-‐scale:
5
y-‐scale:
5
window
that
shows
important
information
related
to
the
story.
Often,
this
means
including
both
the
x-‐
and
y-‐
intercepts.
Good
window
NOT
a
good
window
1
17.
f(x)
=
-‐
x
+
1
18.
7
x
–
3
y
=
14
10
x:
[
,
]
by
y:
[
,
]
x:
[
,
]
by
y:
[
,
]
x-‐scale:
y-‐scale:
x-‐scale:
y-‐scale:
19.
y
=
3(x
–
5)
+12
20.
f
(x)
=
-‐15
(x
+
10)
–
45
x:
[
,
]
by
y:
[
,
]
x:
[
,
]
by
y:
[
,
]
x-‐scale:
y-‐scale:
x-‐scale:
y-‐scale:
V
© 2012 Mathematics Vision Project | M P
In partnership with the Utah State Office of Education
Licensed
under
the
Creative
Commons
Attribution-‐NonCommercial-‐ShareAlike
3.0
Unported
license
Sequences 6
Description:Homework Math 1: Introduction to Arithmetic and Geometric Sequence . A Solidify Understanding Task. Scott has decided to add push-ups to his
