Final answer:
The next number in the first sequence is 13, and the next number in the second sequence is 63.
Step-by-step explanation:
The given sequence: 1, 2, 3, 5, 8 is an example of the Fibonacci sequence. In this sequence, each number is the sum of the two preceding ones. So, to find the next number, we add the last two numbers together. In this case, the next number is 13.
The second sequence given: 1, 3, 7, 15, 31, is an example of a pattern where each number is the result of multiplying the previous number by 2 and then adding 1. To find the next number, we multiply the last number by 2 and add 1. In this case, the next number is 63.