8 The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by \(u _ { 1 } = 1\) and \(u _ { n + 1 } = u _ { n } + 2 n + 1\).
- Show that \(u _ { 4 } = 16\).
- Hence suggest an expression for \(u _ { n }\).
- Use induction to prove that your answer to part (ii) is correct.