Answer:
Option C.![f(x)=(-81)(-\frac{4}{3})^{x-1}](https://tex.z-dn.net/?f=f%28x%29%3D%28-81%29%28-%5Cfrac%7B4%7D%7B3%7D%29%5E%7Bx-1%7D)
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
![T_{n}=a(r)^{n-1}](https://tex.z-dn.net/?f=T_%7Bn%7D%3Da%28r%29%5E%7Bn-1%7D)
Therefore function which defines the same will be
![f(x)=a(r)^{x-1}](https://tex.z-dn.net/?f=f%28x%29%3Da%28r%29%5E%7Bx-1%7D)
![f(x)=(-81)(-\frac{4}{3})^{x-1}](https://tex.z-dn.net/?f=f%28x%29%3D%28-81%29%28-%5Cfrac%7B4%7D%7B3%7D%29%5E%7Bx-1%7D)
Option C is the correct option.