If p, q, r are in a geometric progression and | vedclass

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(B) Given that $p, q, r$ are in a geometric progression,so $q^2 = pr$. Also,$a, b, c$ are in a geometric progression,so $b^2 = ac$. We need to check i

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Geometric Progression

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(B) Given that $p, q, r$ are in a geometric progression,so $q^2 = pr$. Also,$a, b, c$ are in a geometric progression,so $b^2 = ac$. We need to check if $cp, bq, ar$ are in a geometric progression. For $cp, bq, ar$ to be in a geometric progression,the condition $(bq)^2 = (cp)(ar)$ must hold. Since $b^2 = ac$ and $q^2 = pr$,we have $b^2q^2 = (ac)(pr) = (cp)(ar)$. Thus,$(bq)^2 = (cp)(ar)$,which confirms that $cp, bq, ar$ are in a geometric progression.

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

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