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Mathematics

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

Quadratic Equations

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Answer

S = n(n + 1)

⇒ 420 = n2 + n

⇒ n2 + n - 420 = 0

⇒ n2 + 21n - 20n - 420 = 0

⇒ n(n + 21) - 20(n + 21) = 0

⇒ (n + 21)(n - 20) = 0

⇒ n + 21 = 0 or n - 20 = 0

⇒ n = -21 or n = 20.

Since, n cannot be negative,

∴ n ≠ -21.

Hence, n = 20.

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