Q152 / 270 · NDA 2018 (Phase 2) · Mathematics

If an infinite GP has the first term $x$ and the sum 5 , then which of the following is correct?

  • A
    $\mathrm{x} \lt -10$
  • B
    $-10 \lt \mathrm{x} \lt 0$
  • Correct answer
    C
    $0 \lt x \lt 10$
  • D
    $x \gt 10$

Solution

Sum of an infinite G.P. with first term $x$ and common ratio $r( \lt 1)$ is $s=\frac{x}{1-r}$ From question $s=5$ then, $5=\frac{x}{1-r}$ $\begin{aligned} 1-r & =\frac{x}{5} \\ r & =1-\frac{x}{5} \end{aligned}$ For, $-1 \lt 1-\frac{x}{5} \lt 1$ $\begin{aligned} -2 & \lt -\frac{x}{5} \lt 0 \\ 0 & \lt x \lt 10 \end{aligned}$

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

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