To represent the geometric sequence 6, 18, 54, ..., we first need to identify the first term and the common ratio.
- The first term \( a = 6 \).
- The common ratio \( r = \frac{18}{6} = 3 \).
The general formula for a geometric sequence is given by:
\[ f(n) = a \cdot r^{(n - 1)} \]
Here, \( n \) represents the term number in the sequence.
Substituting the values:
- First term \( a = 6 \)
- Common ratio \( r = 3 \)
So the function can be written as:
\[ f(n) = 6 \cdot 3^{(n - 1)} \]
Now, looking at your options, the correct representation of the geometric sequence is:
- f(x) = 6(3)^{(x-1)}
Since you provided multiple answer choices, none of them exactly match the derived formula \( f(n) = 6 \cdot 3^{(n-1)} \). However, if we need to utilize one of the answers and focusing on correctly expressing powers, the choice that's the closest in spirit (but not exact) is:
\[ \text{f(x) = 6(3)} \quad \text{(assuming the power is evaluated correctly)} \]
Note: You might want to clarify or correct the choices you've provided, as they don't accurately represent the correct format for the geometric sequence function derived.