#### 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.

#### Solution

S = n(n + 1)

Given, S = 420

n(n + 1) = 420

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 cannot be negative.

Hence, n = 20.

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Solution 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. Concept: Quadratic Equations.