Question

If the mean of first $n$ natural numbers is $\frac{5n}{9}$, then $n=$

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

Answer 1

Answer: (C)

$9$

It is given that the mean of first $n$ natural numbers is $\frac{5n}{9}$.
Therefore, $\frac{1+2+3+...+n}{n}=\frac{5n}{9}$
$\Rightarrow \frac{n+1}{2}=\frac{5n}{9}$

$\Rightarrow 9n+9=10n$

$\Rightarrow n=9$