5 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 three terms of the sequence are given by $$u _ { 1 } = 200 \quad u _ { 2 } = 150 \quad u _ { 3 } = 120$$

1. Show that \(p = 0.6\) and find the value of \(q\).
2. Find the value of \(u _ { 4 }\).
3. The limit of \(u _ { n }\) as \(n\) tends to infinity is \(L\). Write down an equation for \(L\) and hence find the value of \(L\).