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.

Answer 1

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.