Answer:
To identify the pattern in the given sequence of numbers (5, 7, 12, 20, 31), we can try finding the differences between consecutive terms:
7 - 5 = 2
12 - 7 = 5
20 - 12 = 8
31 - 20 = 11
We notice that the differences themselves form a sequence of consecutive odd numbers: 2, 5, 8, 11. This suggests that the pattern in the original sequence might involve adding consecutive odd numbers to the previous term.
Starting with 5, we can add the first odd number (1) to get 6, then the next odd number (3) to get 9, then the next odd number (5) to get 14, and so on. Continuing this pattern, we get:
5, 7, 12, 20, 31, 45, 62, 82, ...
Therefore, the pattern in the given sequence is that each term is obtained by adding consecutive odd numbers to the previous term, starting with 5 and the first odd number (1).