Question

Write a function to represent the geometric sequence 6, 18, 54, .... (1 point)
• f(x) = 6(3)*-1
• f(x) = 6(3)*
• f(x) = 3(6)*
• f(x) = 3(6)*-1

Answer 1

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

1. The first term \( a = 6 \).
2. 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.