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# How many terms are there in a geometric series if the first term is 5, the common ratio is 3, and the sum of the series is 65?

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How many terms are there in a geometric series if the first term is 5, the common ratio is 3, and the sum of the series is 65?

n=3

n=4

n=5

n=6

Jan 29, 2018

### 1+0 Answers

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Sum of a geometric series is given by

First term [  1 -  common ratio^n ] / [ 1 - common ratio]

Where n is the sum of the first n terms

So we have

65 = 5 [ 1 - 3^n ] / [ 1 - 3 ]       simplify

65 = 5 [ 1 - 3^n ] / -2       multiply by -1 on top/bottom of rthe right side

65 = 5 [ 3^n - 1] / 2            multiply both sides by 2/5

26  =  3^n - 1         add 1 to both sides

27  =  3^n

Because  3^3  = 27......then   n  = 3 terms   Jan 29, 2018