Question

For the following geometric sequence, find the recursive formula.
{-80, 20, -5, ...}

Answer 1

Divides by -4 throughout
common ratio/r=-1/4
ar^(n-1), where a is the first term
substitute all the numbers in it
-80(-1/4)^(n-1)

Answer 2

`a_n =-(1)/(4) \cdot a_(n-1)`

Explanation:

{-80, 20, -5, ...}

General recusive formula for geometric sequence is

`a_n = r \cdot a_(n-1)`

Where 'r' is the common ratio

To find common ratio 'r' we divide second term by first term

`r=(20)/(-80) =-(1)/(4)`

Replace 'r' with -1/4

First term is -80

Recursive formula becomes

`a_n =-(1)/(4) \cdot a_(n-1)`