Discussion
The sum of first 9 terms of an A.P. is 81 and sum of first 18 terms is 324. Find the sum of first 27 terms.
Answer: A
Given \(S_9=81\) and \(S_{18}=324\). Notice that \(81=9^2 \times 1\) and \(324=18^2 \times 1\). No, that's not right. Let's use the formula. \(\frac{9}{2}(2a+8d)=81 \Rightarrow 2a+8d=18\). \(\frac{18}{2}(2a+17d)=324 \Rightarrow 2a+17d=36\). Subtracting the two equations gives \(9d=18 \Rightarrow d=2\). Then \(2a+16=18 \Rightarrow 2a=2 \Rightarrow a=1\). We need \(S_{27} = \frac{27}{2}[2(1)+(26)2] = \frac{27}{2}[2+52] = \frac{27}{2}(54) = 27 \times 27 = 729\).
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