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the first three terms of a GP are the first, fourth and tenth terms of an AP. given that the first term is 6 and that all the terms of a GP are different, find the common ratio.

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  1. a = 6
    ar = a+3d
    ar^2 = a+9d
    so,
    d = (ar-a)/3

    ar^2 = a+9a(r-1)/3
    r^2 = 1+3r-3
    r^2-3r+2 = 0
    r = 1 or 2

    since the GP terms are different, r=2 and d=2 and the sequences are

    6,12,24
    6,8,10,12,14,16,18,20,22,24

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  2. The first ,second and sixth term of an ap and the first three terms of a gp .findthe possible values of the common ratio of the gp

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