N2023 P1 Q2

The first four terms of a sequence are given by \(u_1=10\), \(u_2=61\), \(u_3=206\) and \(u_4=469\). It is given that \(u_n\) is a cubic polynomial.

1. Find \(u_n\) in terms of \(n\).[3]
2. Find the range of values of \(n\) for which \(u_n\) is greater than \(25\,000\).[2]