3 The \(n\)th term of a sequence is \(u _ { n }\).
The sequence is defined by
$$u _ { n + 1 } = k u _ { n } + 12$$
where \(k\) is a constant.
The first two terms of the sequence are given by
$$u _ { 1 } = 16 \quad u _ { 2 } = 24$$
- Show that \(k = 0.75\).
- Find the value of \(u _ { 3 }\) and 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 \(L\).