AnswersDHS Algebra 2 VGeometric Series

Geometric Series Answers

0 verified answers3 views
1
Free Preview

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
2
Free Preview

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
3

A high-interest savings account pays 5.5% interest compounded annually. If $300 is deposited initially and again at the first of each year, which summation represents the money in the account 10 years after the initial deposit?

A
Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 300 (0.055) Superscript n minus 1
Option A
B
Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 305.5 (1.055) Superscript n minus 1
Option B
C
Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 316.5 (0.055) Superscript n minus 1
Option C
D
Sigma-Summation Underscript n = 1 Overscript 10 EndScripts 316.5 (1.055) Superscript n minus 1
Option D
4

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
5

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
6

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
7

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
8

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
9

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
10

What is the value of a1 of the geometric series?

Question illustration
A
Negative twelve-ninths
Option A
B
Negative one-ninths
Option B
C
1
D
12

Did you find these answers helpful?