Q198 / 270 · NDA 2021 (Phase 1) · Mathematics

If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?

  • A
    $-500$
  • Correct answer
    B
    $-250$
  • C
    $500$
  • D
    $250$

Solution

Let common difference $=d$. Then, sum of first 5 terms $=\frac{\text { Sum of next } 5 \text { terms }}{4}$ $\begin{aligned} & \Rightarrow \frac{1}{2} \cdot 5(4+4 \cdot d)=\frac{1}{4} \cdot \frac{1}{2} \cdot 5\{(2+5 \cdot d)+4 \cdot d\} \\ & \Rightarrow 4 \times 4(1+d)=4+14 d\end{aligned}$ $\therefore d=-6 \text {. }$ $\therefore$ Sum of first ten terms$ $=\frac{1}{2} \times 10\{(2 \times 2+9(-6)\}=-250.$

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

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