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AP Calculus

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The 9th term of an arithmetic progression is 4+5p and the sum of the four terms of the progression is 7p-10, where p is a constant.
Given that common difference of the progression is 5, find the value of p.

  • AP Calculus -

    a+8d = 4+5p
    d = 5, so

    a+40 = 4+5p

    I assume you mean the sum of the *first* 4 terms is 7p-10,so

    4/2 (a + a+3d) = 7p-10
    2(2a+15) = 7p-10
    4a + 30 = 7p-10

    So, rearranging things a bit, we have

    a - 5p = -36
    4a - 7p = -40

    13p = 104
    p = 8
    a = 4

    so, the sequence is

    4,9,14,19,24,29,34,39,44,49

    9th term is 4+40 = 44
    sum of 1st 4 terms is 46 = 56-10

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