2020 SJI P2 Q5

The arithmetic sequence \(\{u_n\},\ n\in\mathbb Z^+\) has first term \(u_1=1.6\) and common difference \(d=1.5\).

The geometric sequence \(\{v_n\},\ n\in\mathbb Z^+\) has first term \(v_1=3\) and common ratio \(r=1.2\).

1. Find an expression for \(u_n-v_n\) in terms of \(n\).[2]
2. List all the possible values of \(n\) for which \(u_n>v_n\).[3]
3. Find the greatest value of \(u_n-v_n\), giving your answer to 4 significant figures.[2]