Alg3.2.18

The sum of the first n even natural numbers is given by the relation $S=n(n+1)\,$ .Find n, if the sum is 420.

Given that $n(n+1)=420\,$

Solving the quadratic equation,we get

$n^2+n-420=0,n^2+21n-20n-420=0,n(n+21)-20(n+21)=0\,$

$(n+21)(n-20)=0\,$

$n=-21,20\,$

Since n is a natural number,the value of n is $20\,$