Question

Find the average of squares of first 11 consecutive even numbers.

• A. $184$
• B. $148$
• C. $186$
• D. $174$

Answer 1

The correct option is A $184$

First 11 consecutive Even numbers are

$2,4,6,-----22$

Average of their squares $=\frac{2^3+4^2+6^2+----+{22}^2}{11}$

$=\frac{2^2(1^2+2^2+3^2+---+{11}^2)}{11}$

$=\frac{4}{11}\frac{\left(11\right)\left(12\right)\left(23\right)}{6}=184$

(using formula $1^2+2^2+3^2+---+n^2=\frac{n(n+1)(2n+1)}{6})$