- A sequence is given by:
$$\begin{aligned}
& x _ { 1 } = 1
& x _ { n + 1 } = x _ { n } \left( p + x _ { n } \right)
\end{aligned}$$
where \(p\) is a constant ( \(p \neq 0\) ) .
- Find \(x _ { 2 }\) in terms of \(p\).
- Show that \(x _ { 3 } = 1 + 3 p + 2 p ^ { 2 }\).
Given that \(x _ { 3 } = 1\),
- find the value of \(p\),
- write down the value of \(x _ { 2008 }\).