Question

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

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
f left parenthesis x right parenthesis equals 6 left parenthesis 3 right parenthesis superscript x minus 1 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)=3(6)x
f left parenthesis x right parenthesis equals 3 left parenthesis 6 right parenthesis superscript x baseline

Answer 1

To represent the geometric sequence 6, 18, 54, ..., we first identify the first term and the common ratio of the sequence.

1. The first term \( a_1 \) is 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 formula for the nth term of a geometric sequence is given by:
\[
a_n = a_1 \cdot r^{n-1}
\]
where \( n \) is the term number starting from 1.

In this case, substituting \( a_1 = 6 \) and \( r = 3 \):
\[
a_n = 6 \cdot 3^{n-1}
\]

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

So, the correct response is:
**f(x) = 6(3)^{x-1}**