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We are given a sequence: 18, 6, 2, \(\frac{2}{3}\), \(\frac{2}{9}\), and so on. This appears to be a geometric sequence because the ratio between consecutive terms is constant.

### Step 1: Finding the common ratio
- The first term is \(18\).
- The second term is \(6\), so the ratio between the first and second terms is:
  \[
  \frac{6}{18} = \frac{1}{3}.
  \]
- The third term is \(2\), so the ratio between the second and third terms is:
  \[
  \frac{2}{6} = \frac{1}{3}.
  \]

Thus, the common ratio \(r\) of this geometric sequence is \(\frac{1}{3}\).

### Step 2: Formula for the general term of a geometric sequence
The general term \(S(n)\) of a geometric sequence is given by:
\[
S(n) = a \cdot r^{n-1},
\]
where:
- \(a\) is the first term,
- \(r\) is the common ratio, and
- \(n\) is the position of the term.

In this case:
- \(a = 18\) (the first term),
- \(r = \frac{1}{3}\) (the common ratio).

Thus, the formula for this sequence is:
\[
S(n) = 18 \left( \frac{1}{3} \right)^{n-1}.
\]

### Step 3: Matching with the options
- The correct function is represented by option **D**: 
  \[
  S(n) = 18 \left( \frac{1}{3} \right)^{n-1}.
  \]

Would you like further details or explanations? Here are five related questions for more practice:

1. How do you identify whether a sequence is arithmetic or geometric?
2. What is the sum formula for a finite geometric series?
3. What happens if the common ratio \(r > 1\) in a geometric sequence?
4. How would you find the sum of an infinite geometric series?
5. How can you find the 10th term of a geometric sequence given the first term and common ratio?

**Tip**: In a geometric sequence, the ratio between consecutive terms remains constant, which makes it easy to identify and derive the general term formula.

Which function represents the sequence 18, 6, 2, 2/3, 2/9, ..., where n is a positive whole number?

Learn how to represent the sequence 18, 6, 2, 2/3, 2/9,... as a geometric sequence. This problem covers key concepts such as identifying the first term, common ratio, and using the geometric sequence formula to find the general term. Suitable for students in Grades 9-11.

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