4. A sequence \(\left\{ u _ { n } \right\}\), where \(n \geqslant 0\), satisfies the recurrence relation $$u _ { n + 1 } = \frac { 3 } { 2 } u _ { n } - 2 n ^ { 2 } - 4 \quad u _ { 0 } = k$$ where \(k\) is an integer.

1. Determine an expression for \(u _ { n }\) in terms of \(n\) and \(k\).
   (6) Given that \(u _ { 10 } > 5000\)
2. determine the minimum possible value of \(k\).
   (2)