- A sequence of positive numbers is defined by
$$\begin{aligned}
a _ { n + 1 } & = \sqrt { } \left( a _ { n } ^ { 2 } + 3 \right) , \quad n \geqslant 1 ,
a _ { 1 } & = 2
\end{aligned}$$
- Find \(a _ { 2 }\) and \(a _ { 3 }\), leaving your answers in surd form.
- Show that \(a _ { 5 } = 4\)