Q156 / 270 · NDA 2023 (Phase 2) · Mathematics

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

  • A
    2840
  • B
    2780
  • Correct answer
    C
    2920
  • D
    5700

Solution

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

Hence, the correct answer is option: 'C'.

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