General term from a quadratic partial sum, arithmetic proof and a block-sum equation

The sequence \(u_1,u_2,u_3,\ldots\) satisfies \(u_1+u_2+\cdots+u_n=S_n\), where \(S_n=\dfrac{5n^2+n}{2}\) for every positive integer \(n\).

1. Find \(u_n\) in terms of \(n\).[3]
2. Prove that the sequence is an arithmetic progression.[1]

It is also given that

\[\sum_{r=n+1}^{2n}u_r=156+2\sum_{r=1}^{n}u_r\]

3. Determine \(n\).[4]