4 A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$u _ { n } = 3 ^ { 2 n } - 1$$
- Write down the value of \(u _ { 1 }\).
- Show that \(u _ { n + 1 } - u _ { n } = 8 \times 3 ^ { 2 n }\).
- Hence prove by induction that each term of the sequence is a multiple of 8 .