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
Correct answer: 12
Substitute into the sum formula with \(a = 2\) and \(d = 4\).
\[S_n = \frac{n}{2}\left[2a + (n-1)d\right] = \frac{n}{2}\left[4 + 4n - 4\right] = \frac{n}{2}(4n) = 2n^2\]
Setting this equal to 288:
\[2n^2 = 288 \quad\Longrightarrow\quad n^2 = 144 \quad\Longrightarrow\quad n = 12\]
The negative root is discarded because \(n\) counts terms. Checking: the 12th term is \(2 + 11(4) = 46\), and \(\tfrac{12}{2}(2 + 46) = 6 \times 48 = 288\).
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