- A sequence \(a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots\) is defined by
$$\begin{aligned}
a _ { 1 } & = 4
a _ { n + 1 } & = \frac { a _ { n } } { a _ { n } + 1 } , \quad n \geqslant 1 , n \in \mathbb { N }
\end{aligned}$$
- Find the values of \(a _ { 2 } , a _ { 3 }\) and \(a _ { 4 }\)
Write your answers as simplified fractions.
Given that
$$a _ { n } = \frac { 4 } { p n + q } , \text { where } p \text { and } q \text { are constants }$$
- state the value of \(p\) and the value of \(q\).
- Hence calculate the value of \(N\) such that \(a _ { N } = \frac { 4 } { 321 }\)