SOLUTION: The first three terms of a geometric progression are k + 15,k and k - 12 respectively, find the value of k and the sum to infinity.

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Question 1187235: The first three terms of a geometric progression are k + 15,k and k - 12 respectively, find the value of k and the sum to infinity.
Answer by ikleyn(52780) About Me  (Show Source):
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The first three terms of a geometric progression are k + 15,k and k - 12 respectively,
find the value of k and the sum to infinity.
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Since the first three terms of a geometric progression are k + 15,k and k - 12 respectively, 

we have this proportion


    %28k-12%29%2Fk = k%2F%28k%2B15%29.


Cross multiply, simplify and find k


    (k-12)*(k+15) = k^2

     k^2 - 12k + 15k - 180 = k^2

           3k              = 180

            k              = 180/3 = 60.


The first three terms are  75, 60, 48.


The common dofference is  r = 60%2F75 = 4%2F5 = 0.8.


The sum to infinity is  S = a%5B1%5D%2F%281-r%29 = 75%2F%281-0.8%29 = 75%2F0.2 = 375.

Solved.