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16 September, 22:56

What is the first term of the geometric sequence whose fifth term is 1/24 and tenth term is 1/768

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  1. 16 September, 23:24
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    An=a1r^ (n-1)

    given

    a5=1/24

    a10=1/768

    we know that

    a5=1/24=a1r^ (5-1) and

    a10=1/768=a1r^ (10-1)

    so

    1/24=a1r^4

    1/768=a1r^9

    (a1r^9) / (a1r^4) = r^5 = (1/768) / (1/24) = 1/32

    r^5=1/32

    take 5th root of both sides

    r=1/2

    we have

    a5=a1r^4=1/24

    evaluate r^4 or (1/2) ^4

    1/16

    a1 (1/16) = 1/24

    times both sides by 16/1

    a1=16/24

    a1=2/3

    the first term is 2/3
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