geometric progression

if the first and 8th term of a x^-4 and x^52 and the second term is x^t then t:

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  1. seven steps and 56 powers of x
    ... so 8 powers per step

    t = -4 + 8

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  2. given:
    a= x^-4
    ar^7 = x^52

    use substitution:
    (x^-4)r^7 = x^52
    r^7 = x^59
    r = x^(59/7)

    2nd term = ar
    = (x^-4)(x^59/7)
    = x^(31/7)

    matching it with x^t ---> t = 31/7

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