From the question it is given that,
First term a =
![\[27\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8fb0779b73e66b84df7e7930f78ca88e_l3.png "Rendered by QuickLaTeX.com")
![\[{{8}^{th}}~term\text{ }{{a}_{8}}~=\text{ }1/81\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c5a5b9904c0b3d54861ce0a20b9951d0_l3.png "Rendered by QuickLaTeX.com")
Then,
![\[\begin{array}{*{35}{l}} {{a}_{n}}~=\text{ }a{{r}^{n\text{ }\text{ }1}} \\ {{a}_{8}}~=\text{ }a{{r}^{8\text{ }\text{ }1}}~=\text{ }1/81 \\ {{a}_{8}}~=\text{ }a{{r}^{7}}~=\text{ }1/81 \\ a{{r}^{7}}~=\text{ }1/81 \\ 27{{r}^{7}}~=\text{ }1/81 \\ {{r}^{7}}~=\text{ }1/\left( 81\text{ }\times \text{ }27 \right) \\ {{r}^{7}}~=\text{ }1/2187 \\ {{r}^{7}}~=\text{ }1/({{3}^{7}}) \\ r\text{ }=\text{ }1/3 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f8b3bb82546f222de87585feb12f2b96_l3.png "Rendered by QuickLaTeX.com")
So,
![\[\begin{array}{*{35}{l}}</strong> <strong> {{S}_{10}}~=\text{ }a(1\text{ }\text{ }{{r}^{n}})/\left( 1\text{ }\text{ }r \right) \\</strong> <strong> =\text{ }27[1\text{ }\text{ }{{\left( 1/3 \right)}^{10}}]/\left( 1\text{ }\text{ }1/3 \right) \\</strong> <strong> =\text{ }27[1\text{ }\text{ }(1/{{3}^{10}})]/\left( \left( 3\text{ }\text{ }1 \right)/3 \right) \\</strong> <strong> =\text{ }\left( \left( 27\text{ }\times \text{ }3 \right)/2 \right)\text{ }[1\text{ }\text{ }1/{{3}^{10}}] \\</strong> <strong> =\text{ }\left( 81/2 \right)\text{ }[1\text{ }\text{ }1/{{3}^{10}}] \\</strong> <strong>\end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0f3b690b6d0d4b3b483509b59879dede_l3.png "Rendered by QuickLaTeX.com")
The first term of G.P. is
![\[{{8}^{th}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7ce81476cb3150c3afb7ca55c3eebfbd_l3.png "Rendered by QuickLaTeX.com")
![\[1/81\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7372df756c6270023a40888df192bbc0_l3.png "Rendered by QuickLaTeX.com")
![\[10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e13914576c8f07fa7780b4b1aae684d_l3.png "Rendered by QuickLaTeX.com")
From the question it is given that,
First term a =
Then,
So,
