4. A sequence \(x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
x _ { 1 } & = 1
x _ { n + 1 } & = a x _ { n } + 5 , \quad n \geqslant 1
\end{aligned}$$
where \(a\) is a constant.
- Write down an expression for \(x _ { 2 }\) in terms of \(a\).
- Show that \(x _ { 3 } = a ^ { 2 } + 5 a + 5\)
Given that \(x _ { 3 } = 41\)
- find the possible values of \(a\).