We should consider \[a\]to be the initial term and \[r\]to be the normal proportion of the \[G.P.\]

Given, \[a\text{ }=\text{ }\text{ }3\]

Also, we realize that,

\[\begin{align}

& \begin{array}{*{35}{l}}

{{a}_{n}}~=~a{{r}^{n}}^{1}  \\

So,~{{a}_{4~}}=~a{{r}^{3}}~=\text{ }\left( 3 \right)~{{r}^{3}}  \\

\end{array} \\

& {{a}_{2}}~=~a\text{ }{{r}^{1}}~=\text{ }\left( 3 \right)~r \\

\end{align}\]

Then, at that point, from the inquiry, we have

\[\begin{array}{*{35}{l}}

\left( 3 \right)~{{r}^{3}}~=\text{ }{{\left[ \left( 3 \right)~r \right]}^{2}}  \\

\Rightarrow 3{{r}^{3}}~=\text{ }9~{{r}^{2}}  \\

\Rightarrow ~r~=\text{ }3  \\

{{a}_{7}}~=~a~r{{~}^{71~}}=~a~{{r}^{6}}~=\text{ }\left( 3 \right)\text{ }{{\left( 3 \right)}^{6}}~=\text{ }\text{ }{{\left( 3 \right)}^{7}}~=\text{ }2187  \\

\end{array}\]

In this manner, the seventh term of the G.P. is \[\text{ }2187.\]