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The problem asks to find the 9th term of the sequence, where the first three terms are given as:

\[
32, 16, 8, \dots
\]

We can observe that this is a geometric sequence because each term is half of the previous one.

### Step-by-Step Solution:
1. **Identify the common ratio**:  
   To find the common ratio \( r \), divide the second term by the first term:
   \[
   r = \frac{16}{32} = \frac{1}{2}
   \]

2. **Formula for the \( n \)-th term of a geometric sequence**:  
   The general formula for the \( n \)-th term of a geometric sequence is:
   \[
   a_n = a_1 \times r^{n-1}
   \]
   Where:
   - \( a_1 \) is the first term,
   - \( r \) is the common ratio,
   - \( n \) is the term number.

3. **Substitute the known values**:  
   In this case:
   - \( a_1 = 32 \),
   - \( r = \frac{1}{2} \),
   - \( n = 9 \).

   Plug these values into the formula:
   \[
   a_9 = 32 \times \left(\frac{1}{2}\right)^{9-1} = 32 \times \left(\frac{1}{2}\right)^8
   \]

4. **Simplify**:
   \[
   \left(\frac{1}{2}\right)^8 = \frac{1}{256}
   \]
   So:
   \[
   a_9 = 32 \times \frac{1}{256} = \frac{32}{256} = \frac{1}{8}
   \]

Therefore, the 9th term is \( \frac{1}{8} \) or 0.125.

---

Would you like further details on this?  
Here are some related questions for practice:

1. What is the 10th term of this sequence?
2. How would you find the sum of the first 9 terms of this geometric sequence?
3. What happens to the sequence as \( n \) approaches infinity?
4. Can you write the recursive formula for this geometric sequence?
5. How would the sequence change if the common ratio was negative?

**Tip**: Geometric sequences decrease or grow exponentially depending on the common ratio. Always check the ratio carefully!

The first three terms of a sequence are given: 32, 16, 8. Find the 9th term. Write your answer as a decimal or whole number. Round to the nearest thousandth if necessary.

This problem focuses on finding the 9th term of a geometric sequence with the first three terms: 32, 16, 8. Explore key concepts like the geometric sequence formula, how to determine the common ratio, and step-by-step calculation to arrive at the 9th term. Suitable for Grades 7-10.

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