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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