SOLUTION: the sum of the first six terms of a geometric progression is nine time the sum of the first three terms, where neither the first nor the common ratio is equal to zero. find the com

Question 277454: the sum of the first six terms of a geometric progression is nine time the sum of the first three terms, where neither the first nor the common ratio is equal to zero. find the common ratio.
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
the sum of the first six terms of a geometric progression is nine time the sum of the first three terms, where neither the first nor the common ratio is equal to zero. find the common ratio.



Let the first term be  and the common ratio be 

Sum of first three terms = 

Let this sum of the first three terms be 

Sum of first six terms = 

Sum of first six terms = 

We are given that .  Divide through by X and we have









Check: Suppose the first term is a. Then the first six terms are

a,2a,4a,8a,16a,32a

The sum of the first three terms is a+2a+4a = 7a

The sum of the first 6 terms is a+2a+4a+8a+16a+32a=63a which is 9 times 7a.

So the answer is r=2.

Edwin

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