SOLUTION: Three consecutive terms of a geometric progression are x,x+6 and x+9.Find the value of x.

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Question 1186872: Three consecutive terms of a geometric progression are x,x+6 and x+9.Find the value of x.
Answer by ikleyn(52826) About Me  (Show Source):
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Three consecutive terms of a geometric progression are x,x+6 and x+9.Find the value of x.
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Since the three terms are consecutive terms of a GP, we have this equation


    %28x%2B9%29%2F%28x%2B6%29 = %28x%2B6%29%2Fx.


To solve, cross multiply; then simplify


    x*(x+9) = %28x%2B6%29%5E2

    x^2 + 9x = x^2 + 12x + 36

          9x =       12x + 36

          9x - 12x = 36

            -3x    = 36

              x    = 36%2F%28-3%29 = -12.


The terms are  -12,  -12+6 = -6,  -12 + 9 = -3.


ANSWER.  The terms are  -12, -6, -3.

Solved.