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
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 6, 18, 54, ... we first identify the common ratio and the first term.

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

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

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

Where:

• \( a \) is the first term,
• \( r \) is the common ratio,
• \( n \) is the term number.

For this sequence, as \( x \) is typically treated as the term index starting from 1 (first term being \( x = 1 \)), we have:

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

Thus, the correct function that represents the given geometric sequence is:

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

So the correct response is:

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