NCERT Solution
Class 11
Mathematics
Sequence and Series
show that the products of the corresponding terms...

Question:
Show that the products of the corresponding terms of the sequences a,ar,ar², ...ar^n-1 and A, AR, AR², ,,,AR^n-1form a G.P, and find the common ratio.

Answer:

It has to be proved that the sequence, aA, arAR, ar²AR², …ar^n–1AR^n–1, forms a G.P.

$fraction numerator S e c o n d space t e r m over denominator F i r s t space t e r m end fraction space equals space fraction numerator a r A R over denominator a A end fraction equals r R fraction numerator T h i r d space t e r m over denominator S e c o n d space t e r m end fraction space equals space fraction numerator a r squared A R squared over denominator a r A R end fraction equals r R$

Thus, the above sequence forms a G.P. and the common ratio is rR.

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Question:
Show that the products of the corresponding terms of the sequences a,ar,ar², ...ar^n-1 and A, AR, AR², ,,,AR^n-1form a G.P, and find the common ratio.

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Question: Show that the products of the corresponding terms of the sequences a,ar,ar2, ...arn-1 and A, AR, AR2, ,,,ARn-1 form a G.P, and find the common ratio.

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Question:
Show that the products of the corresponding terms of the sequences a,ar,ar², ...ar^n-1 and A, AR, AR², ,,,AR^n-1form a G.P, and find the common ratio.