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 \(u _ { 1 } = 60\) and \(u _ { 2 } = 48\).
The limit of \(u _ { n }\) as \(n\) tends to infinity is 12 .

1. Show that \(p = \frac { 3 } { 4 }\) and find the value of \(q\).
2. Find the value of \(u _ { 3 }\).