By finding an expression for the \(n\)th term of the series, or otherwise, show that this is a geometric series, and state the values of the first term and the common ratio.

The sum of the first \(n\) terms of a series is given by the expression
\[\begin{equation*}
6 - \frac{2^{n+1}}{3^{n-1}}.
\end{equation*}\]

By finding an expression for the \(n\)th term of the series, or otherwise, show that this is a geometric series, and state the values of the first term and the common ratio.