Geometric Series

Question 1

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

Revolt · Accepted Answer

–364

Question 2

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?

Revolt · Accepted Answer

19,531

Question 3

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

Revolt · Accepted Answer

a1 = 2 and r = –1

Question 4

Which equation represents the partial sum of the geometric series?

Revolt · Accepted Answer

125 + 25 + 5 + 1

Question 5

What is the sum of the geometric series?

Revolt · Accepted Answer

40

Question 6

What is the value of r of the geometric series?

Revolt · Accepted Answer

0.8

Question 7

What is the sum of the infinite geometric series?

Revolt · Accepted Answer

–6

Question 8

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?

Revolt · Accepted Answer

a 1 = StartFraction 23 Over 100 EndFraction, r = StartFraction 1 Over 100 EndFraction

Question 9

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?

Revolt · Accepted Answer

Sigma-Summation Underscript n = 1 Overscript 5 EndScripts 6 (6) Superscript n minus 1

Question 10

What is the value of a1 of the geometric series?

Revolt · Accepted Answer

12

Geometric Series Answers

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