4. A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
a _ { 1 } & = 4
a _ { n + 1 } & = k \left( a _ { n } + 2 \right) , \quad \text { for } n \geqslant 1
\end{aligned}$$
where \(k\) is a constant.
- Find an expression for \(a _ { 2 }\) in terms of \(k\).
Given that \(\sum _ { i = 1 } ^ { 3 } a _ { i } = 2\),
- find the two possible values of \(k\).