A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{array} { l l }
a _ { n + 1 } = 4 a _ { n } - 3 , & n \geqslant 1
a _ { 1 } = k , & \text { where } k \text { is a positive integer. }
\end{array}$$
- Write down an expression for \(a _ { 2 }\) in terms of \(k\).
Given that \(\sum _ { r = 1 } ^ { 3 } a _ { r } = 66\)
- find the value of \(k\).