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A geometric progression with first term 3 is such that the sum of the first three terms is 9.  Find all possible values of the common ratio.

 May 20, 2020
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The first term of the geometric progression is  3,  the next term is  3r,  and the third term is  3r2.

 

What are the possible r-values if the sum of these three terms is 9?

 

3 + 3r + 3r2  =  9

    1 + r + r2  =  3         [divide by 3]

      r2+ r - 2  =  0         [subtract 3 from both sides and rearrange] 

(r - 1)(r + 2)  =  0

 

Either  r = 1  or  r = -2

 
 May 20, 2020

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