Alg3.2.14

The sum of the first n natural numbers is 276.Find the value of n.

The formula for sum of the first n natural numbers is $S=\frac{n(n+1)}{2}\,$

Given $S=\frac{n(n+1)}{2}=276\,$

$n^2+n-552=0\,$

$x^2+24n-23n-552=0,n(n+24)-23(n+24)=0,(n-23)(n+24)=0\,$

$n=23,-24\,$

Here only positive value is considered.

Therefore,the value of n is $23\,$