# 3, -6, 12, 4, 20 what is the next number in the pattern 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.

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