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
$x_n=x_{n-1}* \frac{-1}{4} , x_1=-80$
or
$x_n=-80*(\frac{-1}{4})^{n-1}$

Answer 2

Answer:

$x_{n+1}=-\frac{x_{n}}{4}$

Step-by-step explanation:

We can get geometric sequence dividing each term by -4

So we will have:

$x_{n+1}=\frac{x_{n}}{-4}=-\frac{x_{n}}{4}$

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

x₁=-80

n = 1

$x_{2}=-\frac{x_{1}}{4}=-\frac{-80}{4}=20$

If x₂ = 20, the next value will be:

$x_{3}=-\frac{x_{2}}{4}=-\frac{20}{4}=-5$

I hope it helps you!