- A sequence is defined by
$$\begin{aligned}
u _ { 1 } & = k
u _ { n + 1 } & = 3 u _ { n } - 12 , \quad n \geqslant 1
\end{aligned}$$
where \(k\) is a constant.
- Write down fully simplified expressions for \(u _ { 2 } , u _ { 3 }\) and \(u _ { 4 }\) in terms of \(k\).
Given that \(u _ { 4 } = 15\)
- find the value of \(k\),
- find \(\sum _ { i = 1 } ^ { 4 } u _ { i }\), giving an exact numerical answer.