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Sagot :
The formula which can be used to describe the sequence of provided series is f(x+1) =-(3/4) × f(x).
What is geometric sequence?
Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.
The relation formula can be used to describe such sequence are,
[tex]f(x+1)=r\times f(x)[/tex]
Here, r is the common ratio.
The given sequence is,
[tex]64, -48, 36, -27, ...[/tex]
In the above sequence, the next term has opposite sign to its previous term. The common ratio between the two terms is,
[tex]r=\dfrac{-48}{64}=-\dfrac{3}{4}\\r=\dfrac{36}{-48}=-\dfrac{3}{4}\\r=\dfrac{-27}{36}=-\dfrac{3}{4}[/tex]
The common ratio of the sequence is -3/4. Put this value in the above formula as,
[tex]f(x+1)=-\dfrac{3}{4}\times f(x)[/tex]
Hence, the formula which can be used to describe the sequence of provided series is f(x+1) =-(3/4) × f(x).
Learn more about the geometric sequence here;
https://brainly.com/question/1509142
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