Question

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

f(x)=3(6)x−1

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 of the sequence is \( a = 6 \).
2. The common ratio \( r \) can be found by dividing the second term by the first term:
\[
r = \frac{18}{6} = 3
\]
3. The general form for the \( n \)-th term of a geometric sequence can be defined as:
\[
a_n = a \times r^{n-1}
\]
where \( a \) is the first term, \( r \) is the common ratio, and \( n \) is the term number.

Putting it all together, the function to represent the geometric sequence is:
\[
f(n) = 6 \cdot 3^{n-1}
\]

Thus, the correct response is:
\[
f(x) = 6(3)^{x - 1}
\]

So the answer is:
**f(x)=6(3)x−1**