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The sum of the firest 9 terms of an A.P is 72 and the sum of the next 9 terms is 71, find the A.P

  • math -

    so the sum of 9 is 72 and
    the sum of 18 = 72+71=143

    (9/2)(2a + 8d) = 72 ---> 2a+8d=16
    (18/2)(2a + 17d) = 143 ---> 2a + 17d = 143/9
    subtract them
    9d = -1/9

    in 2a + 8d = 16
    2a -8/9 = 16
    2a = 152/9
    a= 76/9

    AP is 76/9 , 75/9, 74/9 ....


    check for sum of 9 terms
    first = 76/9
    last = 76/9 + 8(-1/9) = 68/9
    sum(9) = (first+last)(9/2) = (76/9+68/9)(9/2) = 72
    looking good!

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