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.