AnswersFL-1200330-Algebra 2 CRModeling with Exponential and Logarithmic Equations

Geometric Series Answers

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1
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What is the sum of the infinite geometric series?

Question illustration
A
Negative StartFraction 93 Over 16 EndFraction
Option A
B
Negative StartFraction 3 Over 32 EndFraction
Option B
C
–4
D
–6
2
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Which equation represents the partial sum of the geometric series?

Question illustration
A
125 + 25 + 5 + 1
B
25 + 5 + 1 + one-fifth
Option B
C
1 + one-fifth + StartFraction 1 Over 25 EndFraction + StartFraction 1 Over 125 EndFraction
Option C
D
StartFraction 1 Over 125 EndFraction + one-fifth + 5 + 125
Option D
3

What is the sum of the first six terms of the geometric series? 2 – 6 + 18 – 54 + ...

A
–486
B
–364
C
–40
D
122
4

A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. Each replicated organism also replicates at the same rate. At hour one, there is one organism. At hour two, there are five more organisms. How many total organisms are there at hour seven?

A
2,801
B
19,531
C
19,607
D
97,655
5

Two students start a club the first week of school. Each member invites three new members the second week of school. Each of these new members then invites three additional members the following week. If the pattern of each new member inviting three new members each week continues, how many members will be in the club after five weeks?

A
80 students
B
121 students
C
242 students
D
363 students
6

What is the sum of the geometric series?

Question illustration
A
–122
B
–2
C
40
D
54
7

Which geometric series represents 0.4444... as a fraction?

A
One-fourth + StartFraction 1 Over 40 EndFraction + StartFraction 1 Over 400 EndFraction + StartFraction 1 Over 4,000 EndFraction + ellipsis
Option A
B
StartFraction 1 Over 40 EndFraction + StartFraction 1 Over 400 EndFraction + StartFraction 1 Over 4,000 EndFraction + StartFraction 1 Over 40,000 EndFraction + ellipsis
Option B
C
Four-tenths + startFraction 4 Over 100 EndFraction + StartFraction 4 Over 1,000 EndFraction + StartFraction 4 Over 10,000 EndFraction + ellipsis
Option C
D
One-tenth + StartFraction 1 Over 100 EndFraction + StartFraction 1 Over 1,000 EndFraction + StartFraction 1 Over 10,000 EndFraction + ellipsis
Option D
8

What is the sum of the infinite geometric series?

Question illustration
A
–288
B
–216
C
–144
D
–72
9

The formula for the sum of an infinite geometric series, , may be used to convert to a fraction. What are the values of and r?

Question illustration
A
a 1 = StartFraction 23 Over 10 EndFraction, r = one-tenth
Option A
B
a 1 = 23, r = StartFraction 1 Over 100 EndFraction
Option B
C
a 1 = StartFraction 23 Over 100 EndFraction, r = 100
Option C
D
a 1 = StartFraction 23 Over 100 EndFraction, r = StartFraction 1 Over 100 EndFraction
Option D
10

What are the values of and r of the geometric series?1 + 3 + 9 + 27 + 81

Question illustration
A
a 1 = 1 and r = one-third
Option A
B
a 1 = one-third and r = 1
Option B
C
a 1 = 1 and r = 3
Option C
D
a 1 = 3 and r = 1
Option D
11

What are the values of a1 and r of the geometric series? 2 – 2 + 2 – 2 + 2

A
a1 = 2 and r = –2
B
a1 = –2 and r = 2
C
a1 = –1 and r = 2
D
a1 = 2 and r = –1
12

A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. Each replicated organism also replicates at the same rate. At hour one, there is one organism. At hour two, there are five more organisms. How many total organisms are there at hour seven?

A
2,801
B
19,531
C
19,607
D
97,655
13

What is the sum of the geometric series?

Question illustration
A
–122
B
–2
C
40
D
54
14

What is the sum of the first six terms of the geometric series? 2 – 6 + 18 – 54 + ...

A
–486
B
–364
C
–40
D
122
15

What are the values of and r of the geometric series?1 + 3 + 9 + 27 + 81

Question illustration
A
a 1 = 1 and r = one-third
Option A
B
a 1 = one-third and r = 1
Option B
C
a 1 = 1 and r = 3
Option C
D
a 1 = 3 and r = 1
Option D
16

What is the sum of the infinite geometric series?

Question illustration
A
–288
B
–216
C
–144
D
–72
17

Which equation represents the partial sum of the geometric series?

Question illustration
A
125 + 25 + 5 + 1
B
25 + 5 + 1 + one-fifth
Option B
C
1 + one-fifth + StartFraction 1 Over 25 EndFraction + StartFraction 1 Over 125 EndFraction
Option C
D
StartFraction 1 Over 125 EndFraction + one-fifth + 5 + 125
Option D
18

Which geometric series represents 0.4444... as a fraction?

A
One-fourth + StartFraction 1 Over 40 EndFraction + StartFraction 1 Over 400 EndFraction + StartFraction 1 Over 4,000 EndFraction + ellipsis
Option A
B
StartFraction 1 Over 40 EndFraction + StartFraction 1 Over 400 EndFraction + StartFraction 1 Over 4,000 EndFraction + StartFraction 1 Over 40,000 EndFraction + ellipsis
Option B
C
Four-tenths + startFraction 4 Over 100 EndFraction + StartFraction 4 Over 1,000 EndFraction + StartFraction 4 Over 10,000 EndFraction + ellipsis
Option C
D
One-tenth + StartFraction 1 Over 100 EndFraction + StartFraction 1 Over 1,000 EndFraction + StartFraction 1 Over 10,000 EndFraction + ellipsis
Option D
19

What is the sum of the infinite geometric series?

Question illustration
A
Negative StartFraction 93 Over 16 EndFraction
Option A
B
Negative StartFraction 3 Over 32 EndFraction
Option B
C
–4
D
–6
20

A flyer is spread by people at a large conference. Within one hour, the first person gives a stack of flyers to six people. Within the next hour, those six people give a stack of flyers to six new people. If this pattern continues, which summation can be used to calculate the number of people who receive a stack of flyers, not including the initial person, in the first five hours?

A
Sigma-Summation Underscript n = 1 Overscript 5 EndScripts 6 (6) Superscript n minus 1
Option A
B
Sigma-Summation Underscript n = 1 Overscript 5 EndScripts 1 (6) Superscript n minus 1
Option B
C
Sigma-Summation Underscript n = 1 Overscript 5 EndScripts 6 (6) Superscript n
Option C
D
Sigma-Summation Underscript n = 1 Overscript 4 EndScripts 1 (6) Superscript n
Option D

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