Question

The sum $S$ of the first $n$ natural numbers is given by $S=\frac{n(n+1)}{2}$. Find $n$, if the sum $S$ is 276.

Answer 1

Given, $S=\frac{n(n+1)}{2}$.........(1)
And $S=276$..........(2)
$\therefore 276=\frac{n(n+1)}{2}$............From (1) and (2)

$276\times 2=n^2+n$
$n^2+n-552=0$
$n^2+24n-23n-552=0$
$(n-23)(n+24)=0$
$\therefore n=23,-24$

Taking only positive value of $n$
Hence, $n=23$