Answer:
The formula which can be used to describe the sequence is:
[tex]f(x)=-81(\frac{-4}{3})^{x-1}[/tex] ⇒ 3rd answer
Step-by-step explanation:
The terms of the sequence are -81, 108, -144, 192, ...
∵ 108 ÷ -81 = [tex]-\frac{4}{3}[/tex]
∵ -144 ÷ 108 = [tex]-\frac{4}{3}[/tex]
∵ 192 ÷ -144 = [tex]-\frac{4}{3}[/tex]
- 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 [tex]a_{n}=ar^{n-1}[/tex], 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 = [tex]-\frac{4}{3}[/tex]
∴ r = [tex]-\frac{4}{3}[/tex]
- Substitute then in the formula above
∴ [tex]a_{n}=-81(\frac{-4}{3})^{n-1}[/tex]
Assume that [tex]a_{n}[/tex] = f(x)
∴ n = x
∴ [tex]f(x)=-81(\frac{-4}{3})^{x-1}[/tex]
The formula which can be used to describe the sequence is:
[tex]f(x)=-81(\frac{-4}{3})^{x-1}[/tex]
