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The problem asks to find the 12th term of the geometric sequence: 328, -164, 82, ...

We can use the general formula for the \(n\)-th term of a geometric sequence:
\[
a_n = a_1 \cdot r^{(n-1)}
\]
Where:
- \(a_n\) is the \(n\)-th term,
- \(a_1\) is the first term,
- \(r\) is the common ratio,
- \(n\) is the term position.

1. The first term \(a_1 = 328\).
2. The common ratio \(r\) is found by dividing the second term by the first term: 
   \[
   r = \frac{-164}{328} = -\frac{1}{2}
   \]
3. We are asked to find the 12th term, so \(n = 12\).

Let's calculate \(a_{12}\).The 12th term of the geometric sequence is approximately \(-0.1602\).

Would you like further clarification on the steps, or do you have any other questions?

Here are 5 related questions to deepen your understanding:
1. How do you calculate the common ratio in a geometric sequence?
2. What is the formula for the sum of the first \(n\) terms of a geometric sequence?
3. How do you determine if a sequence is geometric or arithmetic?
4. Can the common ratio of a geometric sequence be a fraction or decimal?
5. How does changing the common ratio affect the behavior of the sequence?

**Tip:** For geometric sequences with a negative ratio, the terms alternate in sign (positive, negative, positive, etc.).

Find the 12th term of the geometric sequence 328, -164, 82, ...

Learn how to find the 12th term of a geometric sequence starting with 328, -164, 82. Understand key concepts in algebra and geometric sequences with the formula a_n = a_1 * r^(n-1). Suitable for Grades 9-10.

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