Question

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

Answer 1

We have $S=\frac{n(n+1)}{2}=276$ or $n^2+n-552=0$
This gives $n=\frac{-1+\sqrt{1+2208}}{2},\frac{-1-\sqrt{1+2208}}{2}$
or $n=\frac{-1+\sqrt{2209}}{2},\frac{-1-\sqrt{2209}}{2}$ or $n=\frac{-1+47}{2},\frac{-1-47}{2}$
or n = 23, - 24 . We reject n = - 24 since - 24 is not a natural number Therefore n = 23