Question

If the sum of first n natural numbers is $1/7$ of sum of their square, then n is equal to___.

• A. $8$
• B. $9$
• C. $10$
• D. $7$

Answer 1

The correct option is C $10$

solution:

sum of n natural number is: $\frac{n(n+1)}{2}$

sum of squares of n natural number : $\frac{n(n+1)(2n+1)}{6}$

$\frac{n(n+1)}{2}$ = $\frac{1}{7}$ $\frac{n(n+1)(2n+1)}{6}$

$21$ = $(2n+1)$

$n=10$

hence the correct option: C