5. A sequence of numbers \(a _ { 1 } , a _ { 2 } , a _ { 3 } \ldots\) is defined by
$$\begin{aligned}
& a _ { 1 } = 3
& a _ { n + 1 } = 2 a _ { n } - c \quad ( n \geqslant 1 )
\end{aligned}$$
where \(c\) is a constant.
- Write down an expression, in terms of \(c\), for \(a _ { 2 }\)
- Show that \(a _ { 3 } = 12 - 3 c\)
Given that \(\sum _ { i = 1 } ^ { 4 } a _ { i } \geqslant 23\)
- find the range of values of \(c\).