Discussion

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 \(S_n=288, a=2, d=4\).

\(288 = \frac{n}{2}[2(2) + (n-1)4]\)

\(288 = \frac{n}{2}[4 + 4n - 4]\)

\(288 = \frac{n}{2}[4n] = 2n^2\)

\(n^2 = 288/2 = 144\)

\(n = \sqrt{144} = 12\).

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