6 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
$$u _ { 1 } = - 8 \quad u _ { 2 } = 8 \quad u _ { 3 } = 4$$
- Show that \(q = 6\) and find the value of \(p\).
- Find the value of \(u _ { 4 }\).
- The limit of \(u _ { n }\) as \(n\) tends to infinity is \(L\).
- Write down an equation for \(L\).
- Hence find the value of \(L\).