math

find X if the numbers X+3, 5x-3, and 7x+3 are three consecutive terms of a G.P of positive terms. with this value X and given the X+3, 5x -3 and 7x +3 are the third, fourth and fifth terms of the G.P.. find the sum of the first 8 terms of the progression.

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  1. If GP, then

    (5x-3)/(x+3) = (7x+3)/(5x-3)
    25x^2 - 30x + 9 = 7x^2 + 24x + 9
    18x^2 - 54x = 0
    6x(3x - 9) = 0
    x= 0 or x = 3

    if x = 0
    3rd term = 3
    4th term = -3
    5th term = 3
    ..
    1st term = 3
    2nd term = -3
    sum of any even number of terms = 0

    if x = 3,
    3rd term = 6
    4th term = 12
    5th term = 24
    so r = 2
    t(3) = ar^2 = 6
    a = 3/2

    sum(8) = a(r^8 - 1)/(r-1)
    = (3/2)((2^8 - 1)/(3/2 - 1)
    = (3/2)(255)/(1/2)
    = 765

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  2. The first answer is ok, but for the second answer I got 384 and the book says it's 382.5. I'm really confused

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  3. Well, you got mistakes in the second part

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