Math

For the geometric series, S4/S8 = 1/17. Determine the first three terms of the series if the first term is 3.

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asked by Tom
  1. Sn = a(1-r)^n/(1-r), so

    a(1-r)^4/(1-r) ÷ a(1-r)^8/(1-r) = 1/17
    (1-r)^-4 = 1/17
    (1-r)^4 = 17
    1-r = ∜17
    r = 1-∜17

    I think rather than S4 you meant T4
    S4 is usually used for the sum of the first 4 terms.

    So, now we have
    Tn = ar^(n-1)

    T4/T8 = ar^3/ar^7 = r^-4 = 1/17
    r^4 = 17
    r = ∜17

    Still a bit odd. If T4/T8 = 1/16, then we have r=2, and the first three terms are

    3,6,12

    If I'm off in left field, maybe you can work it from here.

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    posted by Steve

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