math - integers

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The sum of 25 consecutive integers is 1000. What is the smallest integer used as an addendum?

  • math - integers -

    let the first term be a
    clearly d = 1
    sum(n) = (n/2)(2a + (n-1)d)
    1000 = (25/2)(2a + 24(1))
    2000 = 25(2a + 24)
    2000= 50a + 600
    50a = 1400
    a = 1400/50 = 28


    check:
    sum(25) = (25/2)( 56 + 24)
    = 12.5(80) = 1000

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