6 For real constants \(a\) and \(b\), the sequence \(U _ { 1 } , U _ { 2 } , U _ { 3 } , \ldots\) is given by
$$U _ { 1 } = a \text { and } U _ { n } = \left( U _ { n - 1 } \right) ^ { 2 } - b \text { for } n \geqslant 2 .$$
- Determine the behaviour of the sequence in the case where \(a = 1\) and \(b = 3\).
- In the case where \(b = 6\), find the values of \(a\) for which the sequence is constant.
- In the case where \(a = - 1\) and \(b = 8\), prove that \(U _ { n }\) is divisible by 7 for all even values of \(n\).