1. **State the problem:** Find the next two terms in the sequence 19, 20, 22, 25, 29. 2. **Analyze the pattern:** Calculate the differences between consecutive terms: $$20 - 19 = 1$$ $$22 - 20 = 2$$ $$25 - 22 = 3$$ $$29 - 25 = 4$$ 3. **Identify the pattern in differences:** The differences are increasing by 1 each time: 1, 2, 3, 4, ... 4. **Predict the next differences:** The next two differences should be 5 and 6. 5. **Calculate the next terms:** $$\text{Next term} = 29 + 5 = 34$$ $$\text{Term after next} = 34 + 6 = 40$$ 6. **Final answer:** The next two terms are 34 and 40.