The sequence provided is:

3, -9, -54, 6, -18, -108, 12, -36, ...

Let's try to analyze this pattern:

1. The terms alternate between positive and negative.
2. The absolute values of the terms seem to follow a geometric pattern in alternating groups of three.

To break this down:
- The first group (positive) is 3, 6, 12.
- The second group (negative) is -9, -18, -36.
- The next group should again follow the geometric pattern, but alternating in sign.

For the positive terms:
- The absolute values increase by multiplying by 2.
   - 3 → 6 (×2), 6 → 12 (×2), next would be 12 × 2 = 24.
   
For the negative terms:
- The absolute values are also increasing by multiplying by 2.
   - -9 → -18 (×2), -18 → -36 (×2), next would be -36 × 2 = -72.

Thus, the next terms in the sequence are:

**24, -72, ...**

Would you like further details or have any questions?

Here are five related questions:
1. Can you identify the common ratio in the geometric progression?
2. How does the pattern of signs (positive/negative) influence the sequence?
3. What happens if we continue the sequence for 10 more terms?
4. Can we write a general formula for the nth term of this sequence?
5. How would the sequence behave if we changed the multiplier to 3 instead of 2?

**Tip:** Always check for alternating patterns in sequences, especially when terms change signs.

Discover how to solve the sequence 3, -9, -54, 6, -18, -108... by identifying a geometric progression with alternating signs. Learn how the absolute values of terms grow by multiplying by 2 and how the signs alternate. This problem is ideal for students in Grades 9-10 learning about sequences and series.

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