Question

The mean of first n odd natural numbers is n281n281

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

Answer 1

The correct option is B $81$

Since, First $n$ odd integers are:
$1,3,5,.......(2n-1)$
this sequence forms an AP.
$\therefore 1+3+5+....(2n-1)=\frac{n}{2}[1+2n-1]=n^2$ [$\because S_n=\frac{n}{2}[a+l]$]
Mean = $\frac{1+3+5+......+(2n-1)}{n}$
$\Rightarrow \frac{n^2}{81}=\frac{n^2}{n}$
$\Rightarrow \frac{1}{81}=\frac{1}{n}$
$\Rightarrow n=81$
Option B is correct.