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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Sequences and Series

NDA 2019 · Mathematics · Sequences and Series

What is the Fourth term of an AP of n terms whose sum is n(n+1) ?

What is the Fourth term of an AP of nn terms whose sum is n(n+1)?\mathrm{n}(\mathrm{n}+1) ?

Options

  1. A6
  2. B8
  3. C12
  4. D20

Correct answer

B. 8

Step-by-step solution

Given, sum of nn terms (Sn)=n(n+1)\left(S_n\right)=n(n+1) We know, Tn=Sn−Sn−1\mathrm{T}_{\mathrm{n}}=\mathrm{S}_{\mathrm{n}}-\mathrm{S}_{\mathrm{n}-1}=[n(n+1)]−[(n−1)(n−1+1)]=n(n+1)−(n−1)n=n(n+1−n+1)=2n∴ Fourth term, T4=2(4)=8\begin{aligned} & =[\mathrm{n}(\mathrm{n}+1)]-[(\mathrm{n}-1)(\mathrm{n}-1+1)] \\ & =\mathrm{n}(\mathrm{n}+1)-(\mathrm{n}-1) \mathrm{n} \\ & =\mathrm{n}(\mathrm{n}+1-\mathrm{n}+1) \\ & =2 \mathrm{n} \\ & \therefore \text{ Fourth term, } \mathrm{T}_4=2(4)=8\end{aligned}$$
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