Q. If the sum of first $n$ natural numbers is 1/5 times the sum of their squares, then the value of $n$ is
A) 5
B) 6
C) 7
D) 8
Explanation
(c)
Since, $\Sigma n = \left( \frac{1}{5} \right)\Sigma n^{2}$
$\Rightarrow \frac{n(n + 1)}{2} = \frac{1}{5}\frac{n(n + 1)(2n + 1)}{6}$
$\Rightarrow 2n + 1 = 15 \Rightarrow n = 7$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.