(C) Given that $p, q, r$ are in $G.P.$,we have $q^2 = pr$ $(i)$.Given that $a, b, c$ are in $G.P.$,we have $b^2 = ac$ $(ii)$.Multiplying $(i)$ and $(i

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) Given that $p, q, r$ are in $G.P.$,we have $q^2 = pr$ $(i)$.Given that $a, b, c$ are in $G.P.$,we have $b^2 = ac$ $(ii)$.Multiplying $(i)$ and $(ii)$,we get $q^2 b^2 = (pr)(ac)$.This can be rewritten as $(bq)^2 = (cp)(ar)$.Since the square of the middle term is equal to the product of the first and third terms,the sequence $cp, bq, ar$ is in $G.P.$

Class 11 Mathematics Sequences and Series Geometric progression

Easy

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

A
$A.P.$
B
$H.P.$
C
$G.P.$
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Sequences and Series

Subtopic

Geometric progression

In a geometric progression with $n$ terms and a common ratio of $3$,the sum of the $n$ terms is $364$ and the last term is $243$. Find the value of $n$.

Medium

View Solution

If in a geometric progression $\{a_n\}$,$a_1 = 3$,$a_n = 96$ and $S_n = 189$,then the value of $n$ is

Easy

View Solution

The sum of infinite terms of a $G.P.$ is $x$ and on squaring each term of it,the sum becomes $y$. Then the common ratio of this series is:

Medium

View Solution

If $\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}$ and $x \neq 0$,then $a, b, c, d$ are in

View Solution

If the third term of a $G.P.$ is $4$,then the product of its first $5$ terms is:

EasyIIT 1982

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

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

Similar Questions

In a geometric progression with $n$ terms and a common ratio of $3$,the sum of the $n$ terms is $364$ and the last term is $243$. Find the value of $n$.

If in a geometric progression $\{a_n\}$,$a_1 = 3$,$a_n = 96$ and $S_n = 189$,then the value of $n$ is

The sum of infinite terms of a $G.P.$ is $x$ and on squaring each term of it,the sum becomes $y$. Then the common ratio of this series is:

If $\frac{a + bx}{a - bx} = \frac{b + cx}{b - cx} = \frac{c + dx}{c - dx}$ and $x \neq 0$,then $a, b, c, d$ are in

If the third term of a $G.P.$ is $4$,then the product of its first $5$ terms is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module