To find the 6th term of the sequence \( 3, -6, 12, -24, \dots \), we can recognize this as a geometric sequence.

### Step 1: Identify the first term and common ratio
- **First term (\(a_1\))**: \( 3 \)
- **Common ratio (\(r\))**: To find \(r\), divide the second term by the first term:
  \[
  r = \frac{-6}{3} = -2
  \]

### Step 2: Find the 6th term
The general formula for the \(n\)th term of a geometric sequence is:
\[
a_n = a_1 \times r^{n-1}
\]
For the 6th term (\(a_6\)):
\[
a_6 = 3 \times (-2)^{6-1} = 3 \times (-2)^5
\]
\[
a_6 = 3 \times (-32) = -96
\]

### Answer:
The 6th term of the sequence is **-96**.

Would you like further details or have any questions? Here are some related questions you might find interesting:

1. How does the sign of the common ratio affect the sequence?
2. What is the sum of the first 6 terms of this geometric sequence?
3. How would you find the \(n\)th term if the sequence alternated differently?
4. What happens to the sequence if the common ratio is fractional?
5. Can a geometric sequence have a common ratio that is a complex number?

**Tip:** Pay close attention to the sign of the common ratio, as it determines whether the sequence alternates between positive and negative terms.

Discover how to find the 6th term of the sequence 3, -6, 12, -24 using the formula for geometric sequences. This problem involves identifying the first term, calculating the common ratio, and applying the formula for the nth term. Suitable for high school students.

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