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How do i find the common ratio, when the 1st, 2nd and 7th terms of a A.P with common difference 2 are the first three terms of a G.P .

  • arithmetic -

    The first, second, and seventh terms of your AP would be
    a, a+2, and a+12

    but these are supposed to be the first 3 terms of a GP, so
    (x+2)/a = (a+12)/(a+2)
    cross-multiply, the a^2 drops out and you get
    a = 1/2

    now you know your first 3 terms of the GP to be
    1/2, 5/2, and 25/2

    check for common ratio:
    (5/2) ÷ (1/2) = 5
    (25/2) ÷ (5/2) = 5

  • Correction - Typo in arithmetic -

    (x+2)/a = (a+12)/(a+2)

    obviously should have been

    (a+2)/a = (a+12)/(a+2)

  • arithmetic -

    Hey thanks a lot Reiny. I got it..

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