Question

A geometric sequence is defined recursively by `a_n= 4a_(n-1)`, and the first term of the sequence is 0.5, how do you find the explicit formula?

Answer 1

`a_n= 0.5(4)^(n-1)`

Explanation:

Looking at this we have...
`a_n= 4a_(n-1)`

`a_2= 4a_(2-1)`
`a_2= 4a_1`
`a_2= 4*0.5`
`a_2=2`

Since we are told that is a geometric sequence there has to be a `r` or a common ratio:
`r=a_2/a_1`
`r=2/.5=4`

So explicitly written, the formula would be:
`a_n= 0.5(4)^(n-1)`