\[First\text{ }term\text{ }\left( a \right)\text{ }of\text{ }a\text{ }G.P\text{ }=\text{ }27\]

And,

\[{{8}^{th}}~term\text{ }=\text{ }{{t}_{8}}~=\text{ }a{{r}^{8\text{ }-\text{ }1}}~=\text{ }1/81\]

\[\left( 27 \right){{r}^{7}}~=\text{ }1/81\]

\[{{r}^{7}}~=\text{ }1/\left( 81\text{ }x\text{ }27 \right)\]

\[{{r}^{7}}~=\text{ }{{\left( 1/3 \right)}^{7}}\]

\[r\text{ }=\text{ }1/3\text{ }\left( r\text{ }<1 \right)\]

\[{{S}_{n}}~=\text{ }a(1\text{ }-\text{ }{{r}^{n}})/\text{ }1\text{ }-\text{ }r\]

So,

\[Sum\text{ }of\text{ }first\text{ }10\text{ }terms\text{ }=\text{ }{{S}_{10}}\]