(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

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(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

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Sequences and Series

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Geometric progression

If the roots of the equation $3x^3-26x^2+52x-24=0$ are in geometric progression,then the sum of two of its roots is

EasyTS EAMCET 2021

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The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot \dots$ to $\infty$ is equal to

DifficultJEE MAIN 2020

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Suppose the sides of a triangle form a geometric progression with common ratio $r$. Then,$r$ lies in the interval

KVPY 2010

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The geometric mean of $n$ positive terms $x_1, x_2, \dots, x_n$ is equal to:

Easy

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If $a = \sum_{n=0}^\infty x^n$,$b = \sum_{n=0}^\infty y^n$,and $c = \sum_{n=0}^\infty (xy)^n$,where $|x|, |y| < 1$,then which of the following is true?

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

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If the roots of the equation $3x^3-26x^2+52x-24=0$ are in geometric progression,then the sum of two of its roots is

The product $2^{\frac{1}{4}} \cdot 4^{\frac{1}{16}} \cdot 8^{\frac{1}{48}} \cdot 16^{\frac{1}{128}} \cdot \dots$ to $\infty$ is equal to

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