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3 March, 05:22

Find four consecutive odd integers so that the sum of the smallest integer and the largest integer is the same as the sum of all four integers

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  1. 3 March, 05:26
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    Let the four consecutive odd integers be

    2n+1, 2n+3, 2n+5, and 2n+7

    where n is an integer.

    The sum of the smallest and largest integer is

    2n+1 + 2n+7 = 4n + 8

    The sum of all integers is

    2n+1 + 2n+3 + 2n+5 + 2n+7 = 8n + 16

    Because the sum of the smallest and largest integer is equal to the sum of all integers,

    8n + 16 = 4n + 8

    4n = - 8

    n = - 2

    2n+1 = 2*-2 + 1 = - 3

    2n+3 = 2*-2 + 3 = - 1

    2n+5 = 2*-2 + 5 = 1

    2n+7 = 2*-2 + 7 = 3

    Answer:

    The four odd integers are - 3, - 1, 1, and 3
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