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the difference between the eighth and fourth of an AP is 40, if the eighth term is 1½ times the forth time find the common difference and the first of the AP

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asked by Kamara
  1. e = f + 4 d ... 4 d = 40

    3/2 f = f + 40 ... 1/2 f = 40

    1st = f - 3 d

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    posted by R_scott
  2. a+7d - (a+3d) = 40
    4d = 40
    d = 10

    a+7d = (3/2)(a+3d)
    2a + 14d = 3a + 9d
    5d = a
    a = 50

    check: term(8) = 50 + 70 = 120
    term(4) = 50 + 30 = 80
    the difference is 120-80 = 40 , check!
    Is 120 = 1½ of 80 ? Yes, check!

    btw, since it said the difference between term(8) and term(4) is 40
    it could have been term4 - term8 = 40
    in that case d = -10 and a = -50
    it also checks.

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