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23 January, 01:46

What is the average of all the integers from 13 to 37

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  1. 23 January, 04:57
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    1 + 2 + 3 + ... + n = n (n + 1) / 2.

    So:

    13 + 14 + 15 + ... + 37

    = (1 + 2 + 3 + ... + 37) - (1 + 2 + 3 + ... + 12)

    = 37 (37 + 1) / 2 - 12 (12 + 1) / 2

    = 625.

    Since there are 25 integers, the average is 625/25 = 25.
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