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The sum of 16terms oe an A.P is -504,while the sum of its 9terms is -126.Find the sum of its 30terms

  • Math -

    sum of 16 terms is -504 ---> 8(2a + 15d) = -504
    2a + 15d = -63

    sum of 9 terms is -126 --> (9/2)(2a + 8d) = -126
    2a + 8d = -28

    subtract:
    7d = -35
    d=-5
    in 2a+8d=-28
    2a - 40 = -28
    2a = 12
    a=6

    sum(30) = 15(12 + 29(-5)) = -1995

  • Math -

    S16 = 16/2 * (2a+15d) = -504
    S9 = 9/2 * (2a + 8d) = -126

    16a + 120d = -504
    9a + 36d = -126

    Multiply #1 by 9 and #2 by 16, then subtract:

    144a + 1080d = -4536
    144a + 576d = -2016

    504d = -2520
    d = -5
    a = 6

    S30 = 15(2a+29d) = 15(12 - 145) = -1995

  • Math -

    -1995

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