Show that the products of the corresponding terms o the sequences `a ,\ a r ,\ a r^2,ddot,\ a r^(n-1)\ a n d\ A ,\ A R ,\ A R^2,\ ,\ A R^(n-1)\ ` form a G.P. and find the common ratio.

Explanation

It has to be proved that the sequence ,
`aA,arAR,ar^2AR^2,...ar^(n−1)AR^(n−1),` forms a G.P.

(Second Term​)/(First Term)=`(arAR)/(aA)​=rR`

Second Term Third Term​
`=(ar^2AR^2)/(arAR)​=rR`

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