7. The \(n\)th term of a sequence is \(u _ { n }\). The sequence is defined by
$$u _ { n + 1 } = p u _ { n } + q$$
where \(p\) and \(q\) are constants.
The first two terms of the sequence are given by \(u _ { 1 } = 96\) and \(u _ { 2 } = 72\).
The limit of \(u _ { n }\) as \(n\) tends to infinity is 24 .
- Show that \(p = \frac { 2 } { 3 }\).
- Find the value of \(u _ { 3 }\).