1. Problem: Find the next number in the sequence -4, -1, 4, 11, 20, .... 2. To find the next number, observe the pattern of differences between consecutive terms: $$-1 - (-4) = 3$$ $$4 - (-1) = 5$$ $$11 - 4 = 7$$ $$20 - 11 = 9$$ 3. The differences are increasing by 2 each time: 3, 5, 7, 9, ... 4. The next difference should be $$9 + 2 = 11$$ 5. Add this difference to the last term: $$20 + 11 = 31$$ 6. Therefore, the next number in the sequence is **31**. Final answer: 31