Question

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

Answer 1

`(25)/(8)\left((8)/(5)\right)^1=5\\\\(25)/(8)\left((8)/(5)\right)^2=5\cdot(8)/(5)=8\\\\(25)/(8)\left((8)/(5)\right)^3=8\cdot(8)/(5)=12.8\\\\(25)/(8)\left((8)/(5)\right)^4=12.8\cdot(8)/(5)=20.48`

The explicit form:

`a_n=(25)/(8)\left((8)/(5)\right)^n`

The recursive form:

`a_n=\left\{\begin{array}{ccc}a_1=5\\a_(n+1)=(8)/(5)a_n\end{array}\right`