Question

–81, 108, –144, 192, ... Which formula can be used to describe the sequence? f(x) = –81 (4/3) X-1 f(x) = –81 (-3/4) X-1 f(x) = –81 (-4/3) X-1 f(x) = –81 (3/4) X-1

Answer 1

Answer:

Option C.$f(x)=(-81)(-\frac{4}{3})^{x-1}$

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

$T_{n}=a(r)^{n-1}$

Therefore function which defines the same will be

$f(x)=a(r)^{x-1}$

$f(x)=(-81)(-\frac{4}{3})^{x-1}$

Option C is the correct option.

Answer 2

 f(x) = –81 (4/3) X-1 f(x) = –81 (-3/4)