N2010 P1 Q3

The sum, \(S_n\), of the first \(n\) terms of a sequence \(u_1,u_2,u_3,\ldots\) is given by \(S_n=n(2n+c)\), where \(c\) is a constant.

1. Find \(u_n\) in terms of \(c\) and \(n\).[3]
2. Find a recurrence relation of the form \(u_{n+1}=\mathrm f(u_n)\).[2]