what is the averege of all of the integers from 13 to 37?

Question

What is the avere of all of the integers from 13 to 37?

Answer 1

There are (37 - 13 + 1) = 25 terms from 13 to 37.

13 + 14 + 15 + ... + 36 + 37
= summation of n from 13 to 37
= [summation of n from 1 to 37] - [summation of n from 1 to 12]
= [(1 + 37)(37 / 2)] - [(1 + 12)(12 / 2)]
= [(38)(37 / 2)] - [(13)(6)]
= (703) - (78)
= 625

average
= 625 / 25
= 25