Find the rule that links the terms: a constant difference, a constant ratio, squares or cubes, growing differences, or two interleaved patterns. The odd man out is the term that breaks the rule.
1Checklist
Check differences between consecutive terms, then the differences of the differences
Check ratios for geometric growth
Compare terms with squares (1, 4, 9, 16, …) and cubes (1, 8, 27, 64, …) and with n² ± 1
Look at alternate terms separately
For odd man out, test primes, squares, cubes, multiples and digit sums