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.

Answer 1

It has to be proved that the sequence, aA, arAR, ar2AR2 , …arnâ-1 ARn-1, forms a G.P.
$\frac{Second\,\, term }{ First\,\, term }= \frac{arAR }{aA} = rR$
$\frac{Third \,\,term}{Second \,\,term} = \frac{ar2 AR2 }{ arAR} = rR$
Thus, the above sequence forms a G.P. and the common ratio is rR.