4. A sequence is defined by
$$\begin{aligned}
u _ { 1 } & = k , \text { where } k \text { is a constant }
u _ { n + 1 } & = 4 u _ { n } - 3 , n \geqslant 1
\end{aligned}$$
- Find \(u _ { 2 }\) and \(u _ { 3 }\) in terms of \(k\), simplifying your answers as appropriate.
Given \(\sum _ { n = 1 } ^ { 3 } u _ { n } = 18\)
- find \(k\).