5. A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
u _ { 1 } & = 1
u _ { n + 1 } & = k - \frac { 8 } { u _ { n } } \quad n \geqslant 1
\end{aligned}$$
where \(k\) is a constant.
- Write down expressions for \(u _ { 2 }\) and \(u _ { 3 }\) in terms of \(k\).
Given that \(u _ { 3 } = 6\)
- find the possible values of \(k\).