# Problem of the Week Problem E Odd Sum

A sequence consists of $$2022$$ terms. Each term after the first term is $$1$$ greater than the previous term. The sum of the $$2022$$ terms is $$31\,341$$.

Determine the sum of the terms in the odd-numbered positions. That is, determine the sum of every second term starting with the first term and ending with the second last term.

Note:
In solving the above problem, it may be helpful to use the fact that the sum of the first $$n$$ positive integers is equal to $$\tfrac{n(n+1)}{2}$$. That is, $1 + 2 + 3 + \cdots + n = \frac{n(n+1)}{2}$