Question

how do you write an explicit and recursive equation with the sequence of numbers given: 5, 8, 12.8, 20.48????

Answer 1

$\dfrac{25}{8}\left(\dfrac{8}{5}\right)^1=5\\\\\dfrac{25}{8}\left(\dfrac{8}{5}\right)^2=5\cdot\dfrac{8}{5}=8\\\\\dfrac{25}{8}\left(\dfrac{8}{5}\right)^3=8\cdot\dfrac{8}{5}=12.8\\\\\dfrac{25}{8}\left(\dfrac{8}{5}\right)^4=12.8\cdot\dfrac{8}{5}=20.48$

The explicit form:

$a_n=\dfrac{25}{8}\left(\dfrac{8}{5}\right)^n$

The recursive form:

$a_n=\left\{\begin{array}{ccc}a_1=5\\a_{n+1}=\dfrac{8}{5}a_n\end{array}\right$