Question

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

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

Answer 1

Given:
Mean of first n natural number =

$$\begin{gathered} \Rightarrow \frac{1+2+3+...+n}{n}=\frac{5n}{9} \\ \Rightarrow \frac{{\displaystyle \frac{n\left(n+1\right)}{2}}}{n}=\frac{5n}{9} \\ \Rightarrow \frac{n+1}{2}=\frac{5n}{9} \\ \Rightarrow 9n+9=10n \\ \Rightarrow n=9 \end{gathered}$$

Hence, the correct option is (c).