Can you find an arithmetic and a geometric sequence which each have second and fourth terms \[u_2=6 \quad\text{and}\quad u_4=54 \text{ ?}\]

Can you find an arithmetic and a geometric sequence which each have \[u_2=-2, \quad u_3=4 \quad\text{and}\quad u_5=16 \text{ ?}\]

A geometric sequence \(G\) has first term \(8\) and common ratio \(-\frac{1}{2}\). Can you find an arithmetic sequence that has the same first term and two other terms the same as the corresponding terms of \(G\)?

Can you find an arithmetic and a geometric sequence that have four terms in common?