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26 March, 01:25

Find an equation for the nth term of a geometric sequence where the second and fifth terms are - 2 and 16, respectively.

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  1. 26 March, 03:59
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    Hello:

    the nth term of a geometric sequence is:

    Un = Up * r^ (n-p). r is the common ratio

    for : p=5 and n = 2

    U5 = U2 * r^3

    16 = - 2 r^3

    r^3 = - 8

    but : - 8 = (-2) ^3

    so : r = - 2

    Un = U2 * r^ (n-2)

    Un = - 2 * (-2) ^ (n-2) = (-2) ^ (n-2+1)

    the nth term of a geometric sequenceis : Un = (-2) ^ (n-1)
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