How about we take
![\[a\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a3ab43dca3872e69a0c1be257c1ecec8_l3.png "Rendered by QuickLaTeX.com")
to be the initial term and
![\[r\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a1e6023f21df45b456a9cd5898649fe1_l3.png "Rendered by QuickLaTeX.com")
to be the normal proportion of the G.P.
Then, at that point, as indicated by the inquiry, we have
![\[\begin{array}{*{35}{l}} {{a}_{5}}~=~a~{{r}^{51~}}=~a~{{r}^{4}}~=~p~\ldots \text{ }\left( i \right) \\ {{a}_{8~}}=~a~{{r}^{81~}}=~a~{{r}^{7}}~=~q~\ldots \text{ }\left( ii \right) \\ {{a}_{11}}~=\text{ }a~{{r}^{111~}}=~a~{{r}^{10}}~=~s~\ldots \text{ }\left( iii \right) \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-45ae04ade3c50afaf5b9d94903f30b33_l3.png "Rendered by QuickLaTeX.com")
Separating condition
![\[\left( ii \right)\text{ }by\text{ }\left( i \right),\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-34eacf4316170e913a1b7ab6ef584750_l3.png "Rendered by QuickLaTeX.com")
we get
How about we take
to be the initial term and
to be the normal proportion of the G.P.
Then, at that point, as indicated by the inquiry, we have
Separating condition
we get
