What is the sum of the first 10 positive integers?

##55##

The first ##10## positive integers form an arithmetic sequence with initial term ##1## and common difference ##1##.

The sum of a contiguous subsequence of an arithmetic sequence is the number of terms multiplied by the average of the first and last term.

In our case, there are ##10## terms, with average value ##(1+10)/2 = 11/2##.

So the sum of the sequence ##1, 2, 3,..., 10## is:

##10 * 11/2 = 55##