- The sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by
$$u _ { n + 1 } = k - \frac { 24 } { u _ { n } } \quad u _ { 1 } = 2$$
where \(k\) is an integer.
Given that \(u _ { 1 } + 2 u _ { 2 } + u _ { 3 } = 0\)
- show that
$$3 k ^ { 2 } - 58 k + 240 = 0$$
- Find the value of \(k\), giving a reason for your answer.
- Find the value of \(u _ { 3 }\)