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Find the common ratio.

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+3 votes
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in Mathematics by (63.2k points)

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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1 Answer

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Solution:

It has to be proved that the sequence, aA, arAR, ar2AR2, …arn–1ARn–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 Rfraction 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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