1. 255 × 2 + 1 = 511.
2. The terms are 2ⁿ − 1: 16−1, 32−1, 64−1, 128−1, 256−1, 512−1. ✓

Answer: 511.

Same rule as before with larger numbers. Choosing 512 forgets the −1 and is the trap on offer.

Shortcut. Each term is one less than a power of two (16, 32 … 256), so the next is 512 − 1 = 511; every term is odd, which rules out 512 at once.

Common trap. 383 — adding the last gap, 128, again (255 + 128); the gaps double each time (16, 32, 64, 128), so the next is 256.