2025 A-Level H2 Mathematics

A sequence \(u_1, u_2, u_3, \ldots\) is defined by

\(u_1=a,\)
\(u_{r+1}=3u_r+5, r\geqslant 1,\)

where \(a\) is a constant.

1. Find expressions for \(u_2\) and \(u_3\) in terms of \(a\).[2]
2. It is given that \(\displaystyle\sum_{r=1}^{4}u_r=110\). Find the value of \(a\).[3]