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Mathematics

The sum of n successive odd numbers starting from 3 is given by the relation S = n(n + 2). Determine n, if the sum is 168.

Quadratic Equations

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Answer

S = n(n + 2)

⇒ 168 = n2 + 2n

⇒ n2 + 2n = 168

⇒ n2 + 2n - 168 = 0

⇒ n2 + 14n - 12n - 168 = 0

⇒ n(n + 14) - 12(n + 14) = 0

⇒ (n - 12)(n + 14) = 0

⇒ (n - 12) = 0 or (n + 14) = 0

⇒ n = 12 or n = -14.

Since, n cannot be negative,

∴ n ≠ -14.

Hence, n = 12.

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