NDA2025MathematicsStatisticsActual
What is the arithmetic mean of 8^2 , 9^2 , 10^2 , , 15^2 ?
Options
- A133.5
- B135.5
- C137.5
- D139.5
Correct answer
C. 137.5
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