Question

Write a function to represent the geometric sequence 6, 18, 54, . . . .(1 point)
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)=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
f left parenthesis x right parenthesis equals 6 left parenthesis 3 right parenthesis superscript x baseline

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

Answer 1

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

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

The general formula for the \(n\)-th term of a geometric sequence can be expressed as:
\[
a_n = a \cdot r^{n-1}
\]
where \(a\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.

For this sequence:
- \(a = 6\)
- \(r = 3\)

Thus, we can write the function representing the geometric sequence as:
\[
f(x) = 6 \cdot 3^{x-1}
\]

So, the correct response from the options provided would be:
\[
f(x) = 6(3)^{x-1}
\]

This represents the function correctly.