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AP EAMCET · Maths · Sequences and Series

\(2+3+5+6+8+9+\ldots . .+2 n \text { terms }=\)

  1. A \(3 n^2+2 n\)
  2. B \(4 n^2+2 n\)
  3. C \(4 n^2\)
  4. D \(5 n^2+2 n\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(3 n^2+2 n\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { Required sum }=1+2+3+4 \ldots \ldots . \text { upto }(3 n+1) \text { terms } \\ & \quad-(4+7+10 \ldots . n \text { terms })-1 \\ & =\frac{(3 n+1)(3 n+2)}{2}-\frac{n}{2}[8+(n-1) \times 3]-1 \\ & =\frac{9 n^2+9 n+2-3 n^2-5 n-2}{2}=3 n^2+2 n\end{aligned}