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Math Help - Sum of Geometric Progression

  1. #1
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    Sum of Geometric Progression

    Hi guys, need some help with this question:

    The sum of the first 20 terms of a geometric series is 10 and the sum of the first 30 terms is 91, find the sum of the first 10 terms.

    So this is how i did it:

    I tried to find the common ratio:
    S20 = 10
    a(r^20 - 1)/(r-1) = 10
    10(r-1) = a(r^20 - 1)
    (r-1) = (a/10)(r^20 - 1) - EQN 1

    S30 = 91
    a(r^30 - 1)/(r-1) = 91
    Sub. EQN 1 into the above EQN:
    a(r^30 - 1) * 10/a(r^20 - 1) = 91

    THe solution just becomes more and more complicated... =/ is there something wrong? How do I simplify?
    Thanks in advance!
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  2. #2
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    Why not stick with

    \displaystyle \frac{a(r^{20} - 1)}{r - 1} = 10 and \displaystyle \frac{a(r^{30} - 1)}{r - 1} = 91 and divide the second equation by the first. This will eliminate the \displaystyle a and enable you to solve for \displaystyle r.
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