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

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.