Final answer:
By using inductive reasoning, observing the pattern of alternating sequences in the given list, we can conclude that the most probable next number in the sequence is 6.
Step-by-step explanation:
The student is asked to use inductive reasoning to predict the most probable next number in a sequence. Observing the pattern in the sequence given: 6, 13, − 1, 6, − 8, − 1, − 15, − 8, − 22, we see that there are two alternating patterns. The sequence decreases by 7 each time for one pattern and increases by 7 each time for the other pattern.
Following these patterns, the two sub-sequences are:
- 6, − 1, − 8, − 15, − 22 (decreasing by 7)
- 13, 6, − 1 (increasing by 7)
From this, the next number in the first pattern sequence would be − 22 − 7 = − 29. Since the last number in the given sequence is − 22 from the first pattern, we look to the second pattern for the next number, which would be − 1 + 7 = 6. Therefore, the most probable next number in the list is 6.