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

Question

Responses

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
f left parenthesis x right parenthesis equals 6 left parenthesis 3 right parenthesis superscript x baseline

f(x)=6(3)x−1

Answer 1

To represent the geometric sequence given as 6, 18, 54, ..., we first 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 nth term of a geometric sequence is given by:

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

Substituting the values we have:

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

This means that the correct function representing the geometric sequence is:

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

So the correct response is:

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