Determine the next number in the following numerical progression: 

10, 15, 22, 31, 42, ...

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To find the next number in the sequence: 

10, 15, 22, 31, 42, ...

Let's look at the difference between each number:

- From 10 to 15, the difference is 15 − 10 = 5.

- From 15 to 22, the difference is 22 − 15 = 7.

- From 22 to 31, the difference is 31 − 22 = 9.

- From 31 to 42, the difference is 42 − 31 = 11.

Now, let's look at these differences: 5, 7, 9, 11.

We can see that the differences are increasing by 2 each time (5 + 2 = 7, 7 + 2 = 9, 9 + 2 = 11).

Following this pattern, the next difference should be 11 + 2 = 13.

To find the next number in the original sequence, we add this new difference (13) to the last number in the sequence (42):

42 + 13 = 55

So, the next number in the progression is 55.

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