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.