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).
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