Write a function to represent the geometric sequence 6, 18, 54, . . . .(1 point)

Question

Responses

f(x)=6(3)x−1
f left parenthesis x right parenthesis equals 6 left parenthesis 3 right parenthesis superscript x minus 1 baseline

f(x)=3(6)x
f left parenthesis x right parenthesis equals 3 left parenthesis 6 right parenthesis superscript x baseline

f(x)=3(6)x−1
f left parenthesis x right parenthesis equals 3 left parenthesis 6 right parenthesis superscript x minus 1 baseline

f(x)=6(3)x

Answer 1

To represent the geometric sequence 6, 18, 54, ..., we need to identify the first term and the common ratio.

1. The first term \( a = 6 \).
2. The common ratio \( r = \frac{18}{6} = 3 \).

The general formula for the \( n \)-th term of a geometric sequence can be written as:

\[ f(n) = a \cdot r^{(n-1)} \]

Substituting \( a = 6 \) and \( r = 3 \):

\[ f(n) = 6 \cdot 3^{(n-1)} \]

Thus, the correct representation of the sequence is:

f(x) = 6(3)^(x-1)

So the correct response would be:

f(x) = 6(3)^(x-1)