Step 1: Split the series into two alternating sub-series.
Odd-position terms:
3,7,13,21,31
Differences:
+4, +6, +8, +10
Even-position terms:
4,7,13,22,34
Differences:
+3, +6, +9, +12
Step 2: The next even-position term will increase by +15:
34 + 9 = 43