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

How does Terry find the sum so quickly?

Because he tried to make an arithmentic progression with them:

101- the 50th odd number
1- 1st odd number

Sn= (101-1)/2*50=50*50=50^2

151- 75 odd number

Sn= (151-1)/2*75=75*75=75^2, and so on....