5. A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
a _ { 1 } & = k
a _ { n + 1 } & = 5 a _ { n } + 3 , \quad n \geqslant 1 ,
\end{aligned}$$
where \(k\) is a positive integer.
- Write down an expression for \(a _ { 2 }\) in terms of \(k\).
- Show that \(a _ { 3 } = 25 k + 18\).
- Find \(\sum _ { r = 1 } ^ { 4 } a _ { r }\) in terms of \(k\), in its simplest form.
- Show that \(\sum _ { r = 1 } ^ { 4 } a _ { r }\) is divisible by 6 .