Algebra 2 Unit 7 -Series Packet - Dam

UNIT 7:
Series

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SUCCESS CRITERIA
I can… calculate the sum of a series.
I can explain… the difference between a sequence vs. series; finite vs. infinite; and arithmetic vs. geometric.
I can justify… why a geometric series converges or diverges.
I can apply… arithmetic or geometric series to solve real-world problems.

LESSON TABLE OF CONTENTS PG #
7.1 3
7.2 TITLE 4-5
7.3 Sequences 6
7.4 Explicit & Recursive Formulas of Sequences 7
7.5 Sigma Notation 8-9
Series
Application of Sequences & Series 2

Lesson 7.1 - Sequences

Sequence
Finite Sequence
Infinite Sequence

Explicit Formula Explicit Formula
Recursive Formula
Recursive Formula
Write the recursive formula for:
Write the explicit formula for:
1) 26, 30, 34, . .. 5) 144, −24,4, . ..
2) 26, 16, 6, . . .. 6) 25, 30, 34, . ..
3) 5, 20, 80, . .. 7) 3, −4, −11, . ..
4) 64, −16,4, . .. 8) 3, 12, 48, . ..
9) 144, −24, 4, . ..

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Lesson 7.2 - Explicit & Recursive Formulas of Sequences

1) Find the 71st term of the sequence 1, 17, 33, . ..
2) Find the 81st term of the sequence 24, 11, −2, . ..
3) Find the 12th term of the sequence 5, 25, 125, . ..
4) Find the 8th term of the sequence 4, −12, 36, . ..
5) Find the 13th term of the sequence + 7, 3 + 12, 5 + 17, . ..
6) Find the 6th term of the sequence −3 − 1, −10 − 6, −17 − 11, . ..
7) Find the 9th term of the sequence 3 6, −9 11, 27 16, . ..
8) Find the 8th term of the sequence 2 7, 6 8, 18 9, . ..
9) Find the 9th term of the sequence 3 6, −9 11, 27 16, . ..

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10) Write an explicit formula that represents the sequence defined by the given recursive formula.
a) 1 = 8, = 4 −1

b) 1 = 6, = −1 + 3

c) 1 = 80, = − 1 −1
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d) 1 = 4 , = −1 + 5

11) If 1 = 10 and = −1 − 4, then find 6.
12) If 1 = 7 and = 2 −1, then find 5.
13) If 1 = 2 and = ( −1)2 + , then find 4.

14) Write a recursive formula that represents the sequence defined by the given explicit formula.
a) = 5 − 4 ( − 1)

b) = 4 + 3
c) = 2(2 2) −1
d) = −9 2(− ) +1

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Lesson 7.3 - Sigma Notation
Sigma Notation

Write each expression in sigma notation.
1) 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17

2) 100 + 50 + 25+. ..

3) 1 + 2 + 3 +. . . + 99
234 100

Write each expression in sigma notation.
4) ∑5 = 0 (3 + 2)

5) 6 ∑5 = 2 (−7 + 2 2)

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Lesson 7.4 - Series Geometric Series
Arithmetic Series

Evaluate each series. Round to the nearest integer.
1) ∑7 = 2 (3 + 1)
2) ∑7 5= 5 (6 + 10)
3) ∑5 = 1 5000(0.8) −1
4) ∑9 8 = 0 600(0.96) −1
5) ∑2 8= 2 900(0.8) −1

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Lesson 7.5 - Application of Series

1) On Aliza’s 18th birthday, her parents gave her options for her monthly allowance for the next two
years. Aliza plans to not spend any of her allowance during the two-year period.

Option A: $60 each month for two years
Option B: $10 in the first month, $15 in the second month, $20 in the third month,
increasing by $5 each month for two years
Option C: $15 in the first month and increasing by 10% each month for two years

a. Calculate the total value of Aliza’s allowance at the end of the two-year period if she
chooses Option A.

b. Calculate the amount of money Aliza will receive in the 17th month if she chooses Option B.

c. Calculate the total value of Aliza’s allowance at the end of the two-year period if she
chooses Option B.

d. Calculate the amount of money Aliza will receive in the 13th month if she chooses Option C.

e. Calculate the total value of Aliza’s allowance at the end of the two-year period if she
chooses Option C.

f. Which option should Aliza choose to earn the greatest allowance at the end of the two-year
period? Justify your answer.

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2) Josh has some hexagonal tiles. Each side of a tile measures 1 inch. He arranges the tiles in rows,
and then he finds the perimeter of each row of tiles.
a. What is the perimeter of a row of 10 tiles?

b. What is the perimeter of a row of 25 tiles?

c. The perimeter of a row of tiles is 66 inches.
How many tiles are in the row?

3) Timothy and Quinn move to London and start work at the same company on the same day. They
each earn an annual salary of 8000 euros during the first year of employment. The company gives
them a salary increase following the completion of each year of employment. Timothy is paid
using Plan A and Quinn is paid using Plan B.

Plan A: The annual salary increases by 450 euro each year.
Plan B: The annual salary increases by 5% each year.

a. Write down an expression for Timothy’s annual salary during his nth year of employment.

b. Write down an expression for Quinn’s annual salary during his nth year of employment.

c. Who would make more money overall if they work for a total of 15 years?

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