- A sequence of numbers \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
a _ { 1 } & = 3
a _ { n + 1 } & = \frac { a _ { n } - 3 } { a _ { n } - 2 } , \quad n \in \mathbb { N }
\end{aligned}$$
- Find \(\sum _ { r = 1 } ^ { 100 } a _ { r }\)
- Hence find \(\sum _ { r = 1 } ^ { 100 } a _ { r } + \sum _ { r = 1 } ^ { 99 } a _ { r }\)