Question

If the sum of first $n$ natural numbers is $\frac{1}{5}$ times the sum of their squares, then the value of $n$ is

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is C $7$

$\Rightarrow$Sum of first $n$ natural numbers is $\frac{n(n+1)}{2}$.

$\Rightarrow$Sum of the squares of the first $n$ natural numbers is $\frac{n(n+1)(2n+1)}{6}$.

So from the question, we have

$\Rightarrow$$\frac{n(n+1)}{2}=\frac{1}{5}.\frac{n(n+1)(2n+1)}{6}$

$\Rightarrow 2n=14$

$\Rightarrow n=7$