Respuesta :
Answer:
Option C.[tex]f(x)=(-81)(-\frac{4}{3})^{x-1}[/tex]
Step-by-step explanation:
The given sequence is -81, 108, -144, 192,......
We have to get the formula which describes the sequence.
We will get the common factor of this sequence first.
For 1st and second terms
common factor r = -(108)/81 = -12/9 = -4/3
For 2nd and 3rd terms
common factor r = -(144/108) = -16/12 = -4/3
Now we know the explicit formula of an geometric sequence is
[tex]T_{n}=a(r)^{n-1}[/tex]
Therefore function which defines the same will be
[tex]f(x)=a(r)^{x-1}[/tex]
[tex]f(x)=(-81)(-\frac{4}{3})^{x-1}[/tex]
Option C is the correct option.
