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  • Show that the products of the corresponding terms of the sequences a, ar, ar raised to 2, …ar raised to n minus 1 and A, AR, AR raised to 2, … AR raised to n minus 1 form a G.P, and find the common ratio.

20.  Show that the products of the corresponding terms of the sequences

    a,ar, ar^2 , ...ar^{n-1} \: \: and\: \: A ,AR, AR^2 ....AR^{n-1} form a G.P, and find the common ratio.

Answers (1)

best_answer

To prove : aA,arAR,ar^2AR^2,...................     is a GP.

\frac{second \, \, term}{first\, \, term}=\frac{arAR}{aA}=rR

\frac{third \, \, term}{second\, \, term}=\frac{ar^2AR^2}{arAR}=rR

Thus, the above sequence is a GP with common ratio of rR.

 

 

Posted by

seema garhwal

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