64, -48, 36, -27, ... which formula can be used to describe the sequence? o (f(x + 1)=\frac{3}{4}f(x)) o…

64, -48, 36, -27, ... which formula can be used to describe the sequence? o (f(x + 1)=\frac{3}{4}f(x)) o (f(x + 1)=-\frac{3}{4}f(x)) o (f(x)=\frac{3}{4}f(x + 1)) o (f(x)=-\frac{3}{4}f(x + 1))

64, -48, 36, -27, ... which formula can be used to describe the sequence? o (f(x + 1)=\frac{3}{4}f(x)) o (f(x + 1)=-\frac{3}{4}f(x)) o (f(x)=\frac{3}{4}f(x + 1)) o (f(x)=-\frac{3}{4}f(x + 1))

Answer

Explanation:

Step1: Find the common ratio

To find the common ratio $r$ of a geometric - sequence, divide a term by its previous term. Let's take the second term $a_2=-48$ and the first term $a_1 = 64$. Then $r=\frac{a_2}{a_1}=\frac{-48}{64}=-\frac{3}{4}$. In a geometric sequence, the relationship between consecutive terms is $f(x + 1)=r\times f(x)$.

Step2: Determine the formula

Since $r =-\frac{3}{4}$, the formula that describes the relationship between consecutive terms of the sequence is $f(x + 1)=-\frac{3}{4}f(x)$.

Answer:

B. $f(x + 1)=-\frac{3}{4}f(x)$