# What is the average of integers from 25 to 41?

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May 31, 2015

$33 = \frac{25 + 41}{2}$

The average of the terms of a contiguous subsequence of any arithmetic progression is the average of the first and last terms.

To see this, notice that if you remove $25$ and $41$ from your sequence, then the average of the remaining terms is still given by the average of the extreme terms $\frac{26 + 40}{2} = 33$.

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