Respuesta :

with every step the previous value gets multiplied by -1/4
[tex]x_n=x_{n-1}* \frac{-1}{4} , x_1=-80[/tex]
or
[tex]x_n=-80*(\frac{-1}{4})^{n-1} [/tex]
whitneytr12

Answer:

[tex]x_{n+1}=-\frac{x_{n}}{4}[/tex]

Step-by-step explanation:

We can get geometric sequence dividing each term by -4

So we will have:

[tex]x_{n+1}=\frac{x_{n}}{-4}=-\frac{x_{n}}{4}[/tex]

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

x₁=-80

n = 1

[tex]x_{2}=-\frac{x_{1}}{4}=-\frac{-80}{4}=20[/tex]

If x₂ = 20, the next value will be:

[tex]x_{3}=-\frac{x_{2}}{4}=-\frac{20}{4}=-5[/tex]

I hope it helps you!

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