# If the mean of first n natural numbers is

Question:

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

(a) 5
(b) 4
(c) 9
(d) 10

Solution:

Given:

Mean of first $n$ natural number $=\frac{5 n}{9}$

$\Rightarrow \frac{1+2+3+\ldots+n}{n}=\frac{5 n}{9}$

$\Rightarrow \frac{\frac{n(n+1)}{2}}{n}=\frac{5 n}{9}$

$\Rightarrow \frac{n+1}{2}=\frac{5 n}{9}$

$\Rightarrow 9 n+9=10 n$

$\Rightarrow n=9$

Hence, the correct option is (c).