- A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
u _ { n + 1 } & = k u _ { n } - 5
u _ { 1 } & = 6
\end{aligned}$$
where \(k\) is a positive constant.
Given that \(u _ { 3 } = - 1\)
- show that
$$6 k ^ { 2 } - 5 k - 4 = 0$$
- Hence
- find the value of \(k\),
- find the value of \(\sum _ { r = 1 } ^ { 3 } u _ { r }\)