Question

The mean of first n natural numbers is $\frac{5n}{9}$. Find $n$.

• A. $5$
• B. $4$
• C. $9$
• D. None of these

Answer 1

Answer: (C)

$9$

Since, Mean of n natural numbers is $\frac{5n}{9}$
$\therefore$ Mean $=\frac{1+2+3+....+n}{n}$
$\Rightarrow \frac{5n}{9}=\frac{\left[\frac{n(n+1)}{2}\right]}{n}$ [$\because$ 1+2+3+....+n = $\frac{n(n+1)}{2}$]
$\Rightarrow \frac{5n}{9}=\frac{n(n+1)}{2n}$
$\Rightarrow \frac{5n}{9}=\frac{(n+1)}{2}$
$\Rightarrow 10n=9n+9$
$\Rightarrow n=9$
$\therefore$ Option $C$ is correct.