Complete the series: 1, 6, 13, 22, 33, ...

In a number series with growing gaps between terms, first compute the differences between consecutive terms. When those differences themselves increase in a recognizable pattern (here, by a constant step), extend that difference-pattern by one more step and add it to the last given term to find the next term.

1. Find the consecutive differences: 6-1=5, 13-6=7, 22-13=9, 33-22=11.

2. Observe that each difference is 2 more than the previous one (5, 7, 9, 11 - increasing by 2 each time).

3. Extend the pattern: the next difference should be 11+2=13.

4. Add this difference to the last term: 33+13=46.

Checking consistency: the full difference sequence 5, 7, 9, 11, 13 is itself an arithmetic progression with common difference 2, matching the pattern established by the first four gaps, which confirms 46 is the correct next term.