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

Question

Responses

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

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)=6(3)x

Answer 1

To represent the geometric sequence \(6, 18, 54, \ldots\), we first identify the first term and the common ratio.

1. The first term \(a\) is \(6\).
2. The common ratio \(r\) can be found by dividing the second term by the first term: \[ r = \frac{18}{6} = 3 \]

The general form of a geometric sequence can be expressed as: \[ f(x) = a \cdot r^{(x-1)} \] Substituting the values we found: \[ f(x) = 6 \cdot 3^{(x-1)} \]

Now we can match this with the provided options. The correct representation of the geometric sequence is:

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

So the final answer is: f(x) = 6(3)^{x-1}