Question

If the mean of first $n$ odd natural numbers is $\frac{n^2}{81}$ =, then $n$ is equal to

• A. $9$
• B. $81$
• C. $27$
• D. none of these

Answer 1

The correct option is B $81$

Given that,
$\frac{1+3+5+7+...+(2n-1)}{n}=\frac{n^2}{81}$
$\Rightarrow =\frac{\frac{n}{2}(2+(n-1\left)2\right)}{n}=\frac{n^2}{n}=\frac{n^2}{81}\Rightarrow n=81$