+0  
 
0
124
1
avatar

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
Sort: 

1+0 Answers

 #1
avatar+85757 
+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

12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details