Question

The average of the numbers \(5^2,6^2,7^2,\ldots,15^2\) is

• A. 110
• B. 100
• C. 115
• D. 105

Hint:

Use \(\sum n^2=\frac{n(n+1)(2n+1)}6\) for consecutive squares.

Answer 1

The Correct Option is A

There are \[ 15-5+1=11 \] terms. Using \[ \sum_{k=1}^{15}k^2=1240 \] and \[ \sum_{k=1}^{4}k^2=30 \] Therefore, \[ 5^2+6^2+\cdots+15^2 =1240-30 =1210. \] Hence \[ \text{Average} =\frac{1210}{11} =110. \]