Question

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

Answer 1

S = n(n + 1)
Given, S = 420
n(n + 1) = 420
n² + n – 420 = 0
n² + 21n – 20n – 420 = 0
n(n + 21) – 20(n + 21) = 0
(n + 21) (n – 20) = 0
n = -21, 20
Since, n cannot be negative.
Hence, n = 20.