- A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
a _ { 1 } & = 1
a _ { n + 1 } & = \frac { k \left( a _ { n } + 1 \right) } { a _ { n } } , \quad n \geqslant 1
\end{aligned}$$
where \(k\) is a positive constant.
- Write down expressions for \(a _ { 2 }\) and \(a _ { 3 }\) in terms of \(k\), giving your answers in their simplest form.
Given that \(\sum _ { r = 1 } ^ { 3 } a _ { r } = 10\)
- find an exact value for \(k\).