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,
$1+2+\ldots+n=\frac{1}{5}\left(1^{2}+2^{2}++n^{2}\right)$
$\Rightarrow \frac{n(n+1)}{2}=\frac{1}{5}\left[\frac{n(n+1)(2 n+1)}{6}\right]$
$\Rightarrow 15=2 n+1$
$\Rightarrow 2 n=14$
$\Rightarrow n=7$