find the next three terms and identify the sequence of the sequence, +, -12, +18, -24

The given sequence is: \( +12, -12, +18, -24, \dots \)

Let's break down the pattern:

1. The signs alternate between positive and negative.
2. The absolute values of the terms increase by 6: \( 12, 18, 24, \dots \).

### Next Three Terms:
Following the alternating sign and increasing by 6 in absolute value:
- The next term is \( +30 \),
- The term after that is \( -36 \),
- The third next term is \( +42 \).

Thus, the next three terms are: \( +30, -36, +42 \).

### Identifying the Sequence:
This sequence alternates between positive and negative terms, and the absolute values of the terms follow an arithmetic progression with a common difference of 6. Specifically, the absolute values are \( 12, 18, 24, \dots \), with each successive term increasing by 6.

This is an **alternating arithmetic sequence**.

Would you like more details or explanations?

Here are 5 related questions to deepen your understanding:
1. How would you find the 10th term of this alternating sequence?
2. What would happen if the sign pattern was reversed (starting with negative)?
3. Can you generalize a formula for the \(n\)-th term of this sequence?
4. How is this sequence different from a geometric sequence?
5. What happens if the difference between terms changes from 6 to another constant?

**Tip**: When identifying patterns, always check for both arithmetic (constant differences) and geometric (constant ratios) progressions.

find the next three terms and identify the sequence of the sequence, +12, -12, +18, -24

Explore how to find the next three terms in the alternating arithmetic sequence +12, -12, +18, -24. Learn about alternating sequences, the arithmetic progression formula, and step-by-step solutions. This problem is ideal for students in Grades 6-8.

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