[tex] \dfrac{25}{8}\left(\dfrac{8}{5}\right)^1=5\\\\\dfrac{25}{8}\left(\dfrac{8}{5}\right)^2=5\cdot\dfrac{8}{5}=8\\\\\dfrac{25}{8}\left(\dfrac{8}{5}\right)^3=8\cdot\dfrac{8}{5}=12.8\\\\\dfrac{25}{8}\left(\dfrac{8}{5}\right)^4=12.8\cdot\dfrac{8}{5}=20.48 [/tex]
The explicit form:
[tex]a_n=\dfrac{25}{8}\left(\dfrac{8}{5}\right)^n[/tex]
The recursive form:
[tex] a_n=\left\{\begin{array}{ccc}a_1=5\\a_{n+1}=\dfrac{8}{5}a_n\end{array}\right [/tex]
