Question

What is the sum of the first 10 positive integers?

Answer 1

`55`

Explanation:

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`