the sum of first n consecutive positive

[4meonly]

the sum of first n consecutive positive odd integers is n^2. What is the sum of odd integers from 25 to 79, inclusive?
A. 1252
b. 1377
c. 1431
d. 1456
e. 2916

OA is D

[carefreeamit]

25 is 13th odd number and 79 is 40th odd number.
sum of odd integers from 25 to 79, inclusive = sum of odd integers till 79 - sum of odd integers till 23 (remember 25 needs to be included in the total)

= 40^2 - 12^2
= 1600 - 144
= 1456