Sure, let's solve this step-by-step to find the next number in the series.
1. Observe the series: 1, 3, 7, 13, 21, 31.
2. Calculate the differences between consecutive terms:
- 3 - 1 = 2
- 7 - 3 = 4
- 13 - 7 = 6
- 21 - 13 = 8
- 31 - 21 = 10
These differences are: 2, 4, 6, 8, 10.
3. Notice that the differences themselves form an arithmetic sequence with a common difference of 2.
4. To predict the next term in the series, find the next difference:
- The current difference sequence ends in 10, so the next difference will be 10 + 2 = 12.
5. Add this next difference to the last term in the series to find the next term:
- The last term is 31. Adding the next difference: 31 + 12 = 43.
So, the next number in the series is 43.
