To be demonstrated: The grouping,
![\[aA,~arAR,~a{{r}^{2}}A{{R}^{2}},\text{ }\ldots a{{r}^{n}}^{1}A{{R}^{n}}^{1}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d7f864d63c532da14e9a121e181b267b_l3.png "Rendered by QuickLaTeX.com")
shapes a G.P.
Presently, we have
In this way, the above arrangement frames a G.P. also, the normal proportion is
![\[rR.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e9b9566491078c591149eb95abd4e65c_l3.png "Rendered by QuickLaTeX.com")
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.
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.