If p,q,r are in one geometric progression and a,b,c in another geometric progression, then cp,bq,ar

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8. Sequences and Series

easy

If $p,\;q,\;r$ are in one geometric progression and $a,\;b,\;c$ in another geometric progression, then $cp,\;bq,\;ar$ are in

A

$A.P.$

B

$H.P.$

C

$G.P.$

D

None of these

Solution

(c) As $p,\;q,\;r$ are in $G.P.$

$\therefore $${q^2} = pr$…..$(i)$

and $a,\;b,\;c$ are also in $G.P.$

$\therefore $${b^2} = ac$…..$(ii)$

From $(i)$ and $(ii),$ ${q^2}{b^2} = (pr)(ac)$

$ \Rightarrow $${(bq)^2} = (cp)\;.\;(ar)$

Hence $cp,\;bq,\;ar$ are in $G.P.$

Standard 11

Mathematics

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