Final answer:
To predict the next number in the sequence 1, 2, 4, 7, 11, 16, we can use inductive reasoning by finding the differences between the consecutive terms and noticing that the differences are increasing by 1 each time.
Step-by-step explanation:
To find the pattern and use inductive reasoning to predict the next number in the sequence 1, 2, 4, 7, 11, 16, we need to look for the differences between the consecutive terms. Subtracting each term from its previous term gives us the sequence of differences: 1, 2, 3, 4, 5. We notice that the differences are increasing by 1 each time. So, to predict the next number, we add the next difference, which is 6, to the last term, which is 16. Therefore, the next number in the sequence is 22.