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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

Guest Jan 29, 2018
 #1
avatar+86915 
+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

 

 

cool cool cool

CPhill  Jan 29, 2018

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