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The sum of the first three terms of a geometric sequence is 49/ 32 and the sum of the next three terms is 49/ 256 . Find the common ratio and the first term of the sequence?

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  1. a(1-r^3)/(1-r) = 49/32
    a(1-r^6)/(1-r) - 40/32 = 49/256

    a(1-r^3)/(1-r) = 49/32
    a(1-r^6)/(1-r) = 441/256

    divide and you have
    (1-r^3)/(1-r^6) = 8/9
    solve for r (it's just a quadratic in r^3) and then you can find a.

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