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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
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.
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