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
If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.
If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in G.P.