8. A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
a _ { 1 } & = k
a _ { n + 1 } & = 3 a _ { n } + 5 , \quad n \geqslant 1
\end{aligned}$$
where \(k\) is a positive integer.
- Write down an expression for \(a _ { 2 }\) in terms of \(k\).
- Show that \(a _ { 3 } = 9 k + 20\).
- Find \(\sum _ { r = 1 } ^ { 4 } a _ { r }\) in terms of \(k\).
- Show that \(\sum _ { r = 1 } ^ { 4 } a _ { r }\) is divisible by 10 .