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22 March, 13:18

Find the sum of the first five terms of the geometric series in which a2 is - 12 and a5 is 768

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  1. 22 March, 15:01
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    Hello:

    the general term is : an = ap*q^ (n-p) ... q : common ratio

    n=5 and p=2 : a5 = a2*q^ (5-2)

    768 = - 12q^3

    q^3 = 768 / (-12)

    q^3 = - 64

    but : 64 = 4^3

    q^3 = (-4) ^3 ... - 4^3 = ( - 4) ^3

    q = - 4

    calculate the first term : a1

    a2 = a1 q

    a1 = a2/q

    a1 = - 12/-4

    a1 = 3

    the sum of the first five terms is : S = a1 * (1 - q^n) / (1 - q)

    a1 = 3 q = - 4 n = 5

    S = 3 (1 - (-4) ^5) / (1 - (-4)) ... calculate
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