2 The \(n\)th term of a geometric sequence is \(u _ { n }\), where
$$u _ { n } = 3 \times 4 ^ { n }$$
- Find the value of \(u _ { 1 }\) and show that \(u _ { 2 } = 48\).
- Write down the common ratio of the geometric sequence.
- Show that the sum of the first 12 terms of the geometric sequence is \(4 ^ { k } - 4\), where \(k\) is an integer.
- Hence find the value of \(\sum _ { n = 2 } ^ { 12 } u _ { n }\).