Let
![\[a\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a3ab43dca3872e69a0c1be257c1ecec8_l3.png "Rendered by QuickLaTeX.com")
be the initial term and
![\[~r\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8463809e1306d3d1b962f8d60d6f25ba_l3.png "Rendered by QuickLaTeX.com")
be the normal proportion of the G.P.
As per the given condition,
![\[\begin{array}{*{35}{l}} {{a}_{4}}~=~a~{{r}^{3}}~=~x~\ldots \text{ }\left( 1 \right) \\ {{a}_{10}}~=~a~{{r}^{9}}~=~y~\ldots \text{ }\left( 2 \right) \\ {{a}_{16}}^{~}=~a\text{ }{{r}^{15~}}=~z~\ldots \text{ }\left( 3 \right) \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-753a93ff117b379f1f107604fdcc75b5_l3.png "Rendered by QuickLaTeX.com")
On separating (2) by (1), we get
Let
be the initial term and
be the normal proportion of the G.P.
As per the given condition,
On separating (2) by (1), we get
