The sum of the squares of the first 15 positive integers is equal to 1240. What is the sum of the squares of the second 15 positive integers?
2480
3490
6785
8215
Explanation:
Sum of square of n numbers is found using the formula $\dfrac{n × (n + 1) (2n + 1)}{6}$
Sum of 1st 15 numbers = 1240
Sum of squares from 16 to 30 = Sum of squares of 1st 30 +ve integers - Sum of squares of 1st 15 +ve integers.
= $\dfrac{30 × 31 × 61}{6}$ - 1240
= 9455 – 1240
= 8215