# Convert a geometric sequence between recursive and explicit form Exercise

Find the explicit term of the sequences defined as follows.

$$\displaystyle{\begin{cases} u_1=4 \cr \cr u_{n+1}=3u_n \text{ for } n≥1 \end{cases}}$$

$$\displaystyle{\begin{cases} u_1=5 \cr \cr u_{n+1}=\dfrac{2}{3}\cdot u_n \text{ for } n≥1 \end{cases}}$$

$$\displaystyle{\begin{cases} u_1=3 \cr \cr u_{n+1}=-2\cdot u_n \text{ for } n≥1 \end{cases}}$$

$$\displaystyle{\begin{cases} u_1=10 \cr \cr u_{n+1}=2\cdot u_n \text{ for } n≥1 \end{cases}}$$

$$\displaystyle{\begin{cases} u_1=8 \cr \cr u_{n+1}=\dfrac{1}{2}\cdot u_n \text{ for } n≥1 \end{cases}}$$

$$\displaystyle{\begin{cases} u_1=7 \cr \cr u_{n+1}=-3\cdot u_n \text{ for } n≥1 \end{cases}}$$

$$\displaystyle{\begin{cases} u_1=2 \cr \cr u_{n+1}=2\cdot u_n \text{ for } n≥1 \end{cases}}$$