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

Guest Jan 29, 2018

#1**+1 **

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

CPhill Jan 29, 2018