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The first three terms of a GP are also the first,nineth and eleventh terms respectively of an AP. Given that the terms of the GP are all different,find the common ratio r,if the sum to infinity of the GP is 8. Find also the first term and the common difference of the AP.

  • Math -

    Both sequences start with a

    ar = a+8d
    ar^2 = a+10d
    a/1-r = 8

    a = 6
    r = 1/4
    d = -9/16

    a/1-r = 6/(3/4) = 8
    GP: 6 3/2 3/8 ...
    AP: 6 87/16 78/16 69/16 60/16 51/16 42/16 33/16 24/16 15/16 6/16 ...

    Note that 24/16 = 3/2 and 6/16 = 3/8

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