Question

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

Answer 1

with every step the previous value gets multiplied by -1/4

`x_n=x_(n-1)* (-1)/(4) , x_1=-80`
or

`x_n=-80*((-1)/(4))^(n-1)`

Answer 2

`x_(n+1)=-(x_(n))/(4)`

Explanation:

We can get geometric sequence dividing each term by -4

So we will have:

`x_(n+1)=(x_(n))/(-4)=-(x_(n))/(4)`

We can prove it putting the first value in this recursive equation:

x₁=-80

n = 1

`x_(2)=-(x_(1))/(4)=-(-80)/(4)=20`

If x₂ = 20, the next value will be:

`x_(3)=-(x_(2))/(4)=-(20)/(4)=-5`

I hope it helps you!