How does Tarun find the sum so quickly?

Question

Ms. Anuska asked the class to see if they could find the sum of the first 50 odd numbers. As everyone settled down to their addition, Tarun ran to her and said, "The sum is 2,500." Ms. Anuska thought, "Lucky guess," and gave him the task of finding the sum of the first 75 odd numbers. Within 20 seconds, Tarun was back with the correct answer of 5,625.

How does Tarun find the sum so quickly?

Answer 1

The sum of first 'n' odd numbers is (n*n).
So, the sum of first 50 odd numbers is (50*50) i.e. 2550.
The sum of first 75 odd numbers is (75*75) i.e. 5625.