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Arithmetic

The sum of three consecutive terms of a geometric progression is 42, and their product is 512. Find the three terms.

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samuel

  1. use your definitions:
    "The sum of three consecutive terms of a geometric progression is 42"
    ----> a + ar + ar^2 = 42
    a(1 + r + r^2) = 42 **

    "their product is 512" --- a(ar)(ar)^2 = 512
    a^3 r^3 = 512
    (ar)^3 = 8^3
    ar = 8 ***

    divide ** by ***
    (1+r + r^2)/r = 42/8 = 21/4
    4r^2 + 4r + 4 = 21r
    4r^2 - 17r + 4 = 0
    (4r - 1)(r - 4) = 0
    r = 1/4 or r = 4

    if r = 4, in ar= 8 , a = 2
    the 3 terms are 2, 8, and 32
    check: sum = 2+8+32 = 42 ⩗
    product = 2 x 8 x 32 = 512 ⩗

    I will leave it up to you to find the other case.

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    Reiny

  2. Thank you so much for your help,it helps to clear some confusions😃😃

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    Aiya Cecilia

  4. Good method of solving

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    Anu

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