Question

Complete the recursive formula of the geometric sequence {500, 200, 80, 32}​

Answer 1

Answer:(2/5)An-1

Explanation:

Answer 2

`a_n=(2)/(5) a_(n-1)`

`a_1=500`

----------------------or one might prefer the answer so that
`r` is a decimal:

`a_n=0.4 a_(n-1)`

`a_1=500`

Explanation:

The recursive form got a geometric sequence is
`a_n=r \cdot a_(n-1)` with a term given such as the first term,
`a_1`.

`r` can be determined by choosing a term from the sequence and dividing by it's previous term.

That is
`r=(a_2)/(a_1)` or
`(a_3)/(a_2)` or so on...

`r=(200)/(500)=(2)/(5)`

So the recursive form for this sequence is:

`a_n=(2)/(5) a_(n-1)`

`a_1=500`