Expert patterns include polynomial sequences and geometric-arithmetic hybrids. A polynomial sequence might follow n² + n, so the terms are 2, 6, 12, 20 — not immediately obvious unless you try computing n(n+1) for each position.

Some expert puzzles combine operations: multiply by 2 then subtract 1, or add consecutive primes. These resist simple difference-checking, which is the point. You often need to try multiple hypotheses before one sticks. Paper helps.