Question

The formula of the sum of first $n$ natural numbers is $S=\frac{n(n+1)}{2}$. If the sum of first $n$ natural number is $325$, find $n$.

Answer 1

$S=\frac{n(n+1)}{2}=325$

$n(n+1)=650$

$n^2+n-650=0$

$\frac{-1\pm \sqrt{(1{)}^2+4(1\left)\right(650)}}{2\left(1\right)}$

$\frac{-1\pm 51}{2}$

$\frac{-1\pm 51}{2}$ $\frac{-1-51}{2}$

$n=25$

$n\ne -25$ as $n$ is natural number

$n+1=26$

$25$ and $26$.