mathematics

The geometric mean between the first two terms in a geometric sequence is 32. if the third term is 4 find the first term

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  1. let the terms be a, ar, 4

    4a = 32
    a = 8 <---- done here

    Bonus marks:

    ar^2 = 4
    8r^2 = 4
    r^2 = 1/2
    r = ± 1/√2

    terms would be
    8 , 8/√2, 8/√2^2
    8 , 8/√2, 4

    looks good,
    a = 8

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    Reiny
  2. Forget the previous post, I didn't read it carefully
    let the 3 terms be a, ar , ar^2

    geometric mean of first two terms = √(a(ar)) = 32
    a √r = 32 --> a = 32/√r

    also ar^2 = 4 --> a = 4/r^2

    32/√r = 4/r^2
    32r^2 = 4√r
    8r^2 = √r
    64r^3 = r
    r^2 = 1/64
    r = ± 1/8
    from a = 4/r^2
    a = 4(1/64) = 256

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    Reiny

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