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NDA 2012
Exam
NDA
Year
2012
Subject
Mathematics
Chapter
Sequences and Series

NDA 2012 · Mathematics · Sequences and Series

If the sequence \ s_n\ is a geometric progression and s_2s_ 11 =s_p...

If the sequence {sn}\left\{\mathrm{s}_n\right\} is a geometric progression and s2s11=sp s8\mathrm{s}_2\mathrm{s}_{11}=\mathrm{s}_p \mathrm{~s}_8, then what is the value of pp ?

Options

  1. A1
  2. B3
  3. C5
  4. DCan not be determined

Correct answer

C. 5

Step-by-step solution

S2S11=SpS8(ar)(ar⁡10)=ar⁡p−1(ar7)r11=r7+p−1r11=r6+p11=6+pp=5\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}
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