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March 27, 2017

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In a geometric sequence, the fourth term is -4, and the eighth term is -324. What is the tenth term?

  • Math - ,

    t(4) = ar^3 = -4
    t(8) = ar^7 = -324
    divide t(8) by t(4)
    r^4 = 81
    r = 81^(1/4) = ± 3

    if r = +3
    in t(4)
    a(3^3) = -4
    a = -4/27
    t(10) = (-4/27)(3^9) = -2916

    if r = -3
    a = -4/-27 = 4/27
    t(10) = ar^9 = (4/27)(-3)^9 = 4(-729) = -2916

    either way, t(10) = -2916

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