The sum of the first 'n' terms of an A.P. is 288. If the first term is 2 and the common difference is 4, find 'n'.
Answer: B
We use the formula for the sum of an A.P.: \(S_n = \frac{n}{2}[2a + (n-1)d]\).
Given \(S_n=288, a=2, d=4\).
\(288 = \frac{n}{2}[2(2) + (n-1)4]\)
\(288 = \frac{n}{2}[4 + 4n - 4]\)
\(288 = \frac{n}{2}[4n] = 2n^2\)
\(n^2 = 288/2 = 144\)
\(n = \sqrt{144} = 12\).