The patterns you'll meet
Arithmetic — the same amount is added or subtracted each time. 4, 9, 14, 19…
Geometric — each term is multiplied by the same number. 3, 6, 12, 24…
Growing steps — the gaps themselves grow evenly. 2, 5, 10, 17… (+3, +5, +7)
Sum of the last two — Fibonacci style. 2, 3, 5, 8, 13…
Square & triangle numbers — 1, 4, 9, 16… and 1, 3, 6, 10…
Two series braided — alternate terms belong to different runs. 2, 100, 5, 90, 8, 80…
Alternating steps — add, then multiply, then add again. 3, 8, 16, 21, 42…
Easy uses arithmetic only. Medium adds multiplying, growing steps and square numbers.
Hard can throw any of them at you — so the first job becomes working out which kind it is.