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Question: what is the next number in the sequence of 6, 9, 13, 20, 31, ??

The given sequence seems to be increasing in an irregular pattern. But if you observe closely, you can see that there's an increasing pattern in the differences of each pair of numbers. From 6 to 9, the difference is 3. From 9 to 13, the difference is 4. From 13 to 20, the difference is 7. From 20 to 31, the difference is 11. If you observe this pattern, each of these differences (3, 4, 7, 11) are in themselves a series where each number is incremented by 1 more than the previous increment was. The difference between 4 and 3 is 1. The difference between 7 and 4 is 3. The difference between 11 and 7 is 4. There's a clear pattern here, where the increment is 1, then 2, then 3. So, the next increment in the second series would logically be 4. If we add 4 to the last difference in the first series (11), we get 15. Adding this 15 to the last given number in the series (31), we get 46. So the next number in the series should be 46.

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