To represent the geometric sequence 6, 18, 54, ..., we first identify the common ratio and the initial term.
- The first term \( a = 6 \).
- The common ratio \( r \) can be determined by dividing the second term by the first term: \[ r = \frac{18}{6} = 3 \]
The general form of a geometric sequence can be expressed as: \[ f(x) = a \cdot r^{(x-1)} \] where \( a \) is the first term and \( r \) is the common ratio.
For this sequence:
- \( a = 6 \)
- \( r = 3 \)
Thus, we can write the function as: \[ f(x) = 6 \cdot 3^{(x-1)} \]
Now we can match this with the provided options:
- A. \( f (x) = 6(3)x \)
- B. \( f (x) = 3(6)x-1 \)
- C. \( f(x) = 6(3)x-1 \)
- D. \( f(x) = 3(6)x \)
The correct representation, based on our derived function, is: C. \( f(x) = 6(3)^{x-1} \).
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