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Even integer from 2 to 16, inclusive (2, 4, 6, ..., 16) as well as odd integers from 1 to 15, inclusive (1, 3, 5, ..., 15) represent evenly spaced set (aka arithmetic progression). Now, the sum of the elements in any evenly spaced set is the mean (average) multiplied by the number of terms, where the mean of the set is (first+last)/2. (Check Number Theory chapter of Math Book for more: math-number-theory-88376.html)
There are 8 even integers from 2 to 16, inclusive, their sum equals to (first+last)/2*(number of terms)=(2+16)/2*8=72;
There are 8 odd integers from 1 to 15, inclusive, their sum equals to (first+last)/2*(number of terms)=(1+15)/2*8=64;
Re: If m equals the sum of the even integers from 2 to 16 [#permalink]
24 Oct 2014, 03:06
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