Final answer:
To predict the next number in a sequence using inductive reasoning, look for a pattern in the numbers. In sequence a (5, 10, 15, 20, 25), the pattern is adding 5. In sequence b (2, 5, 17, 26), the pattern is increasing differences by 2.
Step-by-step explanation:
To predict the next number in a sequence using inductive reasoning, we look for a pattern in the numbers.
In sequence a (5, 10, 15, 20, 25), each number is obtained by adding 5 to the previous number. So, the next number is 25 + 5 = 30.
In sequence b (2, 5, 17, 26), the pattern is not as straightforward. However, we can observe that the differences between consecutive numbers are increasing by 2 each time. The differences are: 3, 12, 9. The next difference should be 12 + 2 = 14. Adding this difference to the last number in the sequence gives us 26 + 14 = 40. So, the next number in sequence b is 40.