In a number series each term follows a rule. Find the rule from the first few terms, check it against the rest, then apply it.
1Common patterns
Addition or subtraction of a constant (arithmetic series)
Multiplication by a constant (geometric series)
Differences that themselves grow by a constant
Squares, cubes, n(n + 1), n² ± 1
Prime numbers
Two interleaved series (look at alternate terms)
Mixed operations such as ×1 + 1, ×2 + 2, ×3 + 3
2Method
Write the differences between consecutive terms
If the differences are not constant, write the differences of differences
If the terms grow very fast, try ratios
For 'find the wrong number', the rule fits every term except one
Example
2, 6, 12, 20, 30, ? — differences 4, 6, 8, 10 grow by 2, so the next difference is 12 and the answer is 42 (also n(n + 1)).