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Please Help!! Math

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A display of cans on a grocery shelf consists of 20 cans on the bottom, 18 cans in the next row, and so on in an arithmetic sequence, until the top row has 4 cans. How many cans, in total, are in the display?

  • Please Help!! Math - ,

    terms of the sequence:
    20 , 18 , 16 ,...4

    So we have a = 20, d = -2 , t(n) = 4

    t(n) = a + (n-1)d
    4 = 20 + (n-1)(-2)
    -16 = -2n + 2
    2n = 18
    n = 9

    so we need sum of 9 terms
    = (9/2)(first + last)= (9/2)(20 + 4) = 108
    or
    Sum(n) = (n/2)(2a + (n-1)d)
    = (9/2)(40 + 8(-2)) = 108

    check:
    term9 = a = 8d
    = 20 + 8(-2) = 20-16 = 4

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