A geometric series with first term a and common ratio r (|r|<1) has sum S = a/(1-r). If a=5 and S=15, what is r?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

A geometric series with first term a and common ratio r (|r|<1) has sum S = a/(1-r). If a=5 and S=15, what is r?

The sum of a geometric series is S = a/(1 − r). Plug in a = 5 and S = 15: 15 = 5/(1 − r). Multiply both sides by (1 − r): 15(1 − r) = 5, so 1 − r = 5/15 = 1/3. Therefore r = 1 − 1/3 = 2/3. This value also satisfies the convergence condition |r| < 1. So, the ratio is 2/3.

A geometric series with first term a and common ratio r (|r|<1) has sum S = a/(1-r). If a=5 and S=15, what is r?

Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

A geometric series with first term a and common ratio r (|r|<1) has sum S = a/(1-r). If a=5 and S=15, what is r?

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