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

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

\[ a_n = a \cdot r^{n-1} \]

In this case, we can express the function as:

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

where \( x \) corresponds to the term number (1 for the first term, 2 for the second term, etc.).

So, the correct representation from the options provided is:

f(x) = 6(3)^(x−1)