(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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Class 11

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Sequences and Series

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Geometric progression

For a sequence $(t_{n})$,if $s_{n} = 7(3^{n} - 1)$,then $t_{n} =$

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For a sequence,$a_1 = 2$ and $\frac{a_{n+1}}{a_n} = \frac{1}{3}$. Then $\sum_{r=1}^{20} a_r$ is

Easy

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If the sum of $n$ terms of a $G.P.$ is $255$,the $n^{th}$ term is $128$,and the common ratio is $2$,then the first term will be:

Medium

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If $S$ is the sum,$P$ is the product,and $R$ is the sum of the reciprocals of $n$ terms of a geometric progression,then $P^2 = \dots$

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The geometric mean of $7, 7^2, 7^3, \dots, 7^n$ is .....

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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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For a sequence $(t_{n})$,if $s_{n} = 7(3^{n} - 1)$,then $t_{n} =$

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