The given sequence is: 3, -6, 12, -24, ...

This appears to be a **geometric sequence**, where each term is obtained by multiplying the previous term by a constant ratio.

To find the common ratio \( r \), divide the second term by the first term:
\[
r = \frac{-6}{3} = -2
\]
Thus, the common ratio \( r = -2 \).

The formula for the \( n \)-th term of a geometric sequence is:
\[
a_n = a_1 \cdot r^{n-1}
\]
where \( a_1 \) is the first term, and \( r \) is the common ratio.

For the 6th term \( a_6 \):
\[
a_6 = 3 \cdot (-2)^{6-1} = 3 \cdot (-2)^5 = 3 \cdot (-32) = -96
\]

So, the 6th term of the sequence is **-96**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the sum of a geometric sequence?
2. What is the general formula for the sum of the first \( n \) terms of a geometric series?
3. How does the behavior of a geometric sequence change when the common ratio is less than 1?
4. What is the significance of the common ratio in a geometric sequence?
5. Can a geometric sequence have a positive common ratio but alternating signs?

**Tip**: Always double-check the common ratio when working with sequences to ensure accurate term predictions!

Learn how to find the 6th term of the geometric sequence 3, -6, 12, -24 using the geometric sequence formula. The solution demonstrates step-by-step calculations to arrive at the 6th term, which is -96. Suitable for students in Grades 8-10.

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