- Find the value of
$$\sum _ { r = 1 } ^ { \infty } 6 \times ( 0.25 ) ^ { r }$$
(3)
(ii) A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
u _ { 1 } & = 3
u _ { n + 1 } & = \frac { u _ { n } - 3 } { u _ { n } - 2 } \quad n \in \mathbb { N }
\end{aligned}$$
- Show that this sequence is periodic.
- State the order of this sequence.
- Hence find
$$\sum _ { n = 1 } ^ { 70 } u _ { n }$$