arithmetic

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the sum of the first 8 term of an arithmetic progresion is 220,if the third term is 17.Find the sum of the first 6 items

  • arithmetic -

    the third term is 17 ---> a+2d = 17
    a = 17-2d

    sum of first 8 terms = 220
    ---> (8/2)(2a + 7d) = 220
    4(2a + 7d) = 220
    2a + 7d = 55
    2(17-2d) + 7d = 55
    34 - 4d + 7d = 55
    3d = 21
    d = 7
    then a = 3

    sum(6) = 3(6 + 35) = 123

    check:
    terms are: 3 10 17 24 31 38 45 52 ..
    sum(8) = 220
    sum(6) = 123
    all is good

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