arithmetic

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You have 798 cans in 19 rows. If the cans are placed so that each row as 3 fewer cans than the other how many cans are in the bottom row?

  • arithmetic -

    This is an arithmetic series
    You know S19, n=19, d=-3
    You don't know "a".

    S19= (n/2)[2a + (n-1)d]

    798 = 19/2(2a + 18(-3)]
    1596 = 38a - 1026
    2633 = 38a
    a = 69

    So depending on whether your bottom row is the
    first or the 69th, it would be either 69 or
    69 + 18(-3) = 15

    check:
    69 + 66 + 63 + ... + 15 for 19 terms
    = 19(first+last)/2 = (19)(69+15)/2 = 798

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