Question

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

Answer 1

$n^2+n=420$

$n^2+n-420=0$

$n^2+21n-20n-420=0$

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

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

so, n = -21 and 20

but n = 20 as n is positive

so n+ 1 = 21