8. A sequence of terms \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
a _ { 1 } & = 4
a _ { n + 1 } & = k a _ { n } + 3
\end{aligned}$$
where \(k\) is a constant.
Given that
- \(\sum _ { n = 1 } ^ { 3 } a _ { n } = 12\)
- all terms of the sequence are different
find the value of \(k\)
[0pt]
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