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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Sequences and Series

NDA 2024 · Mathematics · Sequences and Series

If the sum of the first n terms of a series is n(2 n+1) , then what...

If the sum of the first nn terms of a series is n(2n+1)n(2 n+1), then what is the nnth term?

Options

  1. A4n−14 n-1
  2. B4n4 n
  3. C4n+14 n+1
  4. D4n+34 n+3

Correct answer

A. 4n−14 n-1

Step-by-step solution

 Here, Sn=n(2n+1)⇒Sn−1=(n−1)(2n−1)nth term⁡=Tn=Sn−Sn−1Tn=n(2n+1)−(n−1)(2n−1)=4n−1\begin{aligned} & \text{ Here, } S_n=n(2 n+1) \Rightarrow S_{n-1}=(n-1)(2 n-1) \\ & n^{\text{th }} \operatorname{term}=T_n=S_n-S_{n-1} \\ & T_n=n(2 n+1)-(n-1)(2 n-1)=4 n-1\end{aligned}
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