One of the ways to find patterns in the sequence of numbers is to examine differences between the adjacent numbers. In this case, we would find that:

2nd - 1st = -6 - 3 = -9

3d - 2nd = 12 - (-6) = 18

Notice that second difference can...

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One of the ways to find patterns in the sequence of numbers is to examine differences between the adjacent numbers. In this case, we would find that:

2nd - 1st = -6 - 3 = -9

3d - 2nd = 12 - (-6) = 18

Notice that second difference can be obtained from the first by multiplication by (-2).

4th - 3rd = 4 - 12 = -8. This is 1 greater than the first difference, -9.

5th - 4th = 20 - 4 = 16. This can be obtained from the previous difference by multiplication by (-2), again.

To continue in this fashion, the next difference, between the 6th and the 5th term, must be greater than -8 by 1. Since -8 + 1 = -7, the 6th term can be obtained by subtracting 7 from the 5th term, 20:

20 - 7 = 13

To get the next, 7th term, multiply (-7) by (-2) and add it to the 6th term: 13 + (-7)(-2) = 13 + 14 = 27.

So the next two numbers in the sequence would be 13 and 27. The longer sequence (check the following numbers using the same pattern) would be

3, -6, 12, 4, 20, 13, 27, 21, 33...

This is one of the possibilities of how the given sequence of numbers is formed. There might be others.