Let's analyze the given pattern:

The sequence is: $-12, 60, -300, 1500, \_, \_$

We observe that each term alternates in sign and appears to be multiplied by a constant.

Let’s calculate the ratios between consecutive terms: $\frac{60}{-12} = -5$ $\frac{-300}{60} = -5$ $\frac{1500}{-300} = -5$

The pattern is clear: each term is multiplied by $-5$ to get the next.

Now, let’s apply this rule to find the next two terms:

1. $1500 \times -5 = -7500$
2. $-7500 \times -5 = 37500$

So, the next two numbers in the pattern are: $-7500, 37500$

Would you like more details or further explanation?

Here are 5 related questions:

1. Can you find a similar pattern with different multiplication factors?
2. What happens if the initial number changes but the ratio remains the same?
3. Can you identify other sequences that alternate in sign like this one?
4. How would this pattern behave if a different factor like $2$ or $10$ was used?
5. Can patterns like this be represented as a geometric sequence?

Tip: When solving number patterns, checking for common ratios or differences can often reveal the underlying rule.