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1 June, 04:07

Identify the 16th term of a geometric sequence where a1 = 4 and a8 = - 8,748.

-172,186,884

-57,395,628

57,395,628

172,186,884

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Answers (1)
  1. 1 June, 06:29
    0
    -57,395,628

    Step-by-step explanation:

    The n-th term of a geometric sequence is given by ...

    an = a1·r^ (n-1)

    Then the ratio of the 8th term to the 1st term is ...

    a8/a1 = (a1·r^ (8-1)) / (a1·r^ (1-1)) = r^7

    and the common ratio is ...

    (-8748/4) ^ (1/7) = - 3

    That makes the 16th term be ...

    a16 = 4· (-3) ^ (16 - 1) = - 57,395,628
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