Question

If the sum of first $n$ natural numbers is $1/5$ times the sum of their squares, then $n$ is equal to

• A. 7
• B. 8
• C. 6
• D. 5

Answer 1

Answer: (A)

According to the given condition,
$1+2+\dots +n=\frac{1}{5}\left(1^2+2^2++n^2\right)$
$\Rightarrow \frac{n(n+1)}{2}=\frac{1}{5}\left[\frac{n(n+1)(2n+1)}{6}\right]$
$\Rightarrow 15=2n+1$
$\Rightarrow 2n=14$
$\Rightarrow n=7$