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

To find the next number in the sequence, we can first examine the differences between consecutive terms: - The difference between 9 and 6 is 3. - The difference between 13 and 9 is 4. - The difference between 20 and 13 is 7. - The difference between 31 and 20 is 11. So, we have the differences: 3, 4, 7, 11. Next, we observe the pattern in these differences to see if there is a second level of difference: - The difference between 4 and 3 is 1. - The difference between 7 and 4 is 3. - The difference between 11 and 7 is 4. So, the pattern of the second level of differences is: 1, 3, 4. If we extend this difference pattern, it appears that each level 2 difference itself increases by 1 each time. Continuing the pattern: - After 4, we expect the next difference to be 5. So, the next difference at level 1 would be: - The last difference at level 1 was 11; adding 5 to 11 gives us 16. Finally, to find the next number in the sequence: - Add 16 (the new difference) to the last number in the sequence (31): 31 + 16 = 47. Thus, the next number in the sequence is 47.

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.