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The sum of first 6 terms of an Arithmetic progression is 6 the product of 2nd term and 5th term is -80 . Find the terms of A.P.

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  1. sum of first 6 terms
    = (6/2)(2a + 5d) = 6
    2a + 5d = 2 ---> a = (2-5d)/2 **

    (a+d)(a+4d) = -89
    a^2 + 5ad + 4d^2 = -80
    sub ** into that
    (2-5d)^2/4 + 5d(2-5d)/2 + 4d^2 = -80
    times 4, the LCD
    (2-5d)^2 + 10d(2-5d) + 16d^2 = -320
    4 - 20d + 25d^2 + 20d - 50d^2 + 16d^2 + 320 = 0
    -9d^2 + 324 = 0
    d^2 = 36
    d = ± 6

    if d = 6, a = (2 - 30)/2 = -14
    terms are: -14, -8, -2, 4, 10, 16, ....

    you do the case when d = -6

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