NDA Mathematics Question (2025) — Solution

Step-by-step solution

The given sequence is 8^2, 9^2, 10^2, , 15^2. Number of terms, n = 15 - 8 + 1 = 8. Sum of the series S = _ k=8 ^ 15 k^2 = _ k=1 ^ 15 k^2 - _ k=1 ^ 7 k^2. Using the formula _ k=1 ^ n k^2 = n(n+1)(2n+1) 6 , _ k=1 ^ 15 k^2 = 15 16 31 6 = 1240 _ k=1 ^ 7 k^2 = 7 8 15 6 = 140 S = 1240 - 140 = 1100 Arithmetic mean = S n = 1100 8 = 137.5 Answer: 137.5