# Convert an arithmetic sequence between recursive and explicit form Exercise

Find the explicit formula of the arithmetic sequences defined as follows. The first term of each sequence is $$\displaystyle{a_1}$$.

$$\displaystyle{{\begin{cases} a_1=4 \cr \cr\forall n \in \mathbb{N}^*,\ a_{n+1}=a_n-2 \end{cases}\\}}$$

$$\displaystyle{\begin{cases} a_3=15 \cr \cr \forall n \in \mathbb{N}^*,\ a_{n+1}=a_n+4 \end{cases}\\}$$

$$\displaystyle{\begin{cases} a_1=-1 \cr \cr \forall n \geq2,\ a_{n+1}=a_{n-1}+6 \end{cases}\\}$$

$$\displaystyle{\begin{cases} a_1=-3 \cr \cr\forall n \in \mathbb{N}^*,\ a_{n+1}=a_n+5 \end{cases}\\}$$

$$\displaystyle{\begin{cases} a_1=0 \cr \cr\forall n \in \mathbb{N}^*,\ a_{n+2}=a_n-10 \end{cases}\\}$$

$$\displaystyle{\begin{cases} a_5=0 \cr \cr\forall n \in \mathbb{N}^*,\ a_{n+1}=a_n+5 \end{cases}\\}$$

$$\displaystyle{\begin{cases} a_1=-4 \cr \cr\forall n\geq2,\ a_{n+5}=a_{n-1}+18 \end{cases}\\}$$