Question

What is the sum of the first 500 odd numbers?

Answer 1

250000

Explanation:

The first one is 1, the last is `2times 500-1 = 999`. Their average is 500. Since the numbers are in an AP, the average of all 500n of them is also the same, namely 500. Thus, the sum is

`500times 500 = 250000`

In general, the sum of the first `n` odd numbers is

`n times 1/2(1+(2n-1)) = n^2`