To identify the next number in the series 1, 4, 10, 19, 31, we first need to observe the differences between consecutive terms.
- 4 – 1 = 3
- 10 – 4 = 6
- 19 – 10 = 9
- 31 – 19 = 12
Now, let’s examine these differences:
- 3
- 6
- 9
- 12
We can see that the differences themselves are changing in a consistent way:
- 6 – 3 = 3
- 9 – 6 = 3
- 12 – 9 = 3
These second differences are constant, which indicates that the original sequence is likely quadratic.
Hence, we can predict that the next difference after 12 will be:
- 12 + 3 = 15
Finally, adding this difference to the last term in the original series:
- 31 + 15 = 46
Therefore, the next number in the series is 46.