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NDA 2015
Exam
NDA
Year
2015
Subject
Mathematics
Chapter
Sequences and Series

NDA 2015 · Mathematics · Sequences and Series

If p, q, r are in one geometric progression and a, b, c are in...

If p,q,r\mathrm{p}, \mathrm{q}, \mathrm{r} are in one geometric progression and a,b,c\mathrm{a}, \mathrm{b}, \mathrm{c} are in another geometric progression, then ap, bq, cr are in

Options

  1. AArithmetic progression
  2. BGeometric progression
  3. CHarmonic progression
  4. DNone of the above

Correct answer

B. Geometric progression

Step-by-step solution

Let the common ratio be K1\mathrm{K}_1 for p,q\mathrm{p}, \mathrm{q} and r . ∴q=K1pr=(K1)2p\begin{aligned} & \therefore \mathrm{q}=\mathrm{K}_1 \mathrm{p} \\ & & \mathrm{r}=\left(\mathrm{K}_1\right)^2 \mathrm{p} \end{aligned} Let the common ratio be K2\mathrm{K}_2 for a,b\mathrm{a}, \mathrm{b} and c ∴b=K2ac=(K2)2a∴bq=(K1K2)apCr=(K1K2)2ap\begin{aligned} & \therefore \mathrm{b}=\mathrm{K}_2 \mathrm{a} \\ & & \mathrm{c}=\left(\mathrm{K}_2\right)^2 \mathrm{a} \\ & \therefore \mathrm{bq}=\left(\mathrm{K}_1 \mathrm{ K}_2\right) \mathrm{ap} \\ & & \mathrm{Cr}=\left(\mathrm{K}_1 \mathrm{ K}_2\right)^2 \mathrm{ap} \end{aligned} So ap, bq, cr are in G.P.
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