### Sequences

Package of problems

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## Problem

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

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

3. 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 $G$?

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