9 For each value of \(k\) the sequence of real numbers \(\left\{ u _ { n } \right\}\) is given by \(u _ { 1 } = 2\) and \(u _ { n + 1 } = \frac { k } { 6 + u _ { n } }\). For each of the following cases, either determine a value of \(k\) or prove that one does not exist.
- \(\left\{ \mathrm { u } _ { n } \right\}\) is constant.
- \(\left\{ \mathrm { u } _ { \mathrm { n } } \right\}\) is periodic, with period 2 .
- \(\left\{ \mathrm { u } _ { \mathrm { n } } \right\}\) is periodic, with period 4 .