Arithmetic Series Answers

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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
4

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
6

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
7

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
8

Which fraction represents the decimal ?

Question illustration
A
One-twelfth
Option A
B
StartFraction 3 Over 25 EndFraction
Option B
C
StartFraction 4 Over 33 EndFraction
Option C
D
StartFraction 33 Over 4 EndFraction
Option D
10

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

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