Find the next and 20th term in the sequence.

1, -3, 2, -5, 4, -7, 8, -9...

This one seems very hard to me. I tried the difference table method, which gives no pattern that I can see.

1 -3 2 -5 4 -7 8 -9

-4 5 -7 9 -11 15 -17

9 -12 16 -20 26 -32

-21 +28 -36 46 58

Only thing I can think of so far is the alternate +ve and -ve values could be solved with (-1)^n, so it gives a negative value for odd powers.

This problem does not seem to be a simple arithmetic or geometric sequence. Can anyone guide towards what area of mathematics this problem is from, and is there a way to think of similar sequence problems?

Thanks.