Q203 / 270 · NDA 2012 (Phase 1) · Mathematics

If the sequence $\left\{\mathrm{s}_n\right\}$ is a geometric progression and $\mathrm{s}_2$ $\mathrm{s}_{11}=\mathrm{s}_p \mathrm{~s}_8$, then what is the value of $p$ ?

  • A
    1
  • B
    3
  • Correct answer
    C
    5
  • D
    Can not be determined

Solution

$\begin{aligned} & \mathrm{S}_2 \mathrm{~S}_{11}=\mathrm{S}_p \mathrm{~S}_8 \\ & (\mathrm{ar})\left(\operatorname{ar}^{10}\right)=\operatorname{ar}^{p-1}\left(\mathrm{ar}^7\right) \\ & r^{11}=r^{7+p-1} \\ & r^{11}=r^{6+p} \\ & 11=6+p \\ & p=5\end{aligned}$

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

Relevant Questions