5. A sequence \(x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots\) is defined by
$$\begin{gathered}
x _ { 1 } = 1 ,
x _ { n + 1 } = a x _ { n } - 3 , n \geqslant 1 ,
\end{gathered}$$
where \(a\) is a constant.
- Find an expression for \(x _ { 2 }\) in terms of \(a\).
- Show that \(x _ { 3 } = a ^ { 2 } - 3 a - 3\).
Given that \(x _ { 3 } = 7\),
- find the possible values of \(a\).