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Question
The sum S of n successive odd numbers starting from 3 is given by the relation: S = n(n + 2). Determine n, if the sum is 168.
Solution
From the given information, we have:
n(n + 2) = 168
n2 + 2n – 168 = 0
n2 + 14n – 12n – 168 = 0
n(n + 14) – 12(n + 14) = 0
(n + 14)(n – 12) = 0
n = –14, 12
But, n cannot be negative.
Therefore, n = 12.
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