Question

–81, 108, –144, 192, ...

Answer 1

Answer:

C.

Step-by-step explanation:

Answer 2

Answer:

The formula which can be used to describe the sequence is:

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

Step-by-step explanation:

The terms of the sequence are -81, 108, -144, 192, ...

∵ 108 ÷ -81 = $-\frac{4}{3}$

∵ -144 ÷ 108 = $-\frac{4}{3}$

∵ 192 ÷ -144 =  $-\frac{4}{3}$

- There is a constant ratio between each two consecutive terms

∴ The sequence is a geometric sequence

The formula of the nth term of the geometric sequence is $a_{n}=ar^{n-1}$, where a is the first term and r is the constant ratio between each two consecutive terms

∵ The first term is -81

∴ a = -81

∵ The constant ratio =  $-\frac{4}{3}$

∴ r =  $-\frac{4}{3}$

- Substitute then in the formula above

∴  $a_{n}=-81(\frac{-4}{3})^{n-1}$

Assume that $a_{n}$ = f(x)

∴ n = x

∴  $f(x)=-81(\frac{-4}{3})^{x-1}$

The formula which can be used to describe the sequence is:

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