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The sum of the first 21 terms of a linear sequence is 28 and the sum of the first 28 terms is 21 . find which term of the sequence is 0 and also the sum of the terms preceeding it

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  1. Use your definitions
    "The sum of the first 21 terms of a linear sequence is 28"
    ---> (21/2)(2a + 20d) = 28
    2a + 20d = 8/3

    "the sum of the first 28 terms is 21"
    ---> (28/2)(2a + 27d) = 21
    2a + 27d = 3/2

    subtract them
    7d = -7/6
    d = -1/6
    2a + 20(-1/6) = 8/3
    2a = 6
    a = 3

    term(n) = 3 + (n-1)(-1/6)
    = 3 - n/6 + 1/6
    = (18 - n + 1)/6 = (19 - n)/6

    so you want (19-n)/6 = 0
    19 = n

    so the 19th term is 0

    now find sum(18)

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    Reiny
  2. It’s complicated and complex

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