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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Sequences and Series

NDA 2023 · Mathematics · Sequences and Series

If the n^ th term of a sequence is (2 n+5)/(7) , then what is the...

If the nth \mathrm{n}^{\text{th }} term of a sequence is 2n+57\frac{2 n+5}{7}, then what is the sum of its first 140 terms?

Options

  1. A2840
  2. B2780
  3. C2920
  4. D5700

Correct answer

C. 2920

Step-by-step solution

Given, tn=2n+57\mathrm{t}_{\mathrm{n}}=\frac{2 \mathrm{n}+5}{7} Since, t140=2×140+57=2857t1=2×1+57=77\mathrm{t}_{140}=\frac{2 \times 140+5}{7}=\frac{285}{7}\mathrm{t}_1=\frac{2 \times 1+5}{7}=\frac{7}{7} Now, $\mathrm{S}_{140}=\frac{140}{2}\left(\mathrm{t}_1+\mathrm{t}_{140}\right)=70\left(\frac{7}{7}+\frac{285}{7}\right)=2920
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