The function which is used to represent the graphed geometric sequence is
[tex]f(x) = 80{( \frac{1}{4}) }^{x - 1} [/tex]
Let a be first term and r common ratio of the Geometric progression.
The Geometric sequence is of the form a,ar,ar^2, ...
The common ratio will be ar/a.
From the graph, we can find out the sequence as 80,20,5, ...
Here we can see that the sequence is in Geometric Progression.
First term a=80
Common ratio r= ar/a
= 20/80
=1/4
General term of Geometric sequence is
[tex]f(x) = a {r}^{x - 1} [/tex]
Substituting the value a = 80 and r = 1/4,
we get,
[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]
Hence, the correct answer is
[tex]f(x) =80 { (\frac{1}{4} )}^{x - 1} [/tex]
Learn more about Geometric sequence here:
https://brainly.com/question/24643676
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