Number and letter series
Test simple differences, ratios, alternating rules, and position patterns before choosing the next term.
Use the simplest complete rule#
For 4, 7, 10, 13, the difference is consistently +3, so the next term is 16. For 3, 6, 12, 24, each term doubles.
If differences themselves change regularly, inspect second differences. For 2, 5, 10, 17, the first differences are 3, 5, 7, so the next difference may be 9.
Alternating patterns#
A sequence may contain two interwoven rules. In 2, 10, 4, 20, 6, 30, the odd positions are 2, 4, 6 and the even positions are 10, 20, 30.
Letter series#
Map letters to alphabet positions when helpful. A, C, F, J advances by 2, 3, and 4 positions. Account carefully for whether the sequence wraps after Z.
Common mistakes#
Do not accept a rule that fits only the last pair. Avoid unnecessarily complex patterns when a simpler rule explains all terms. Check whether the question asks for the next, missing, or incorrect term.
Final method#
Write the change between each pair, test one operation, inspect alternating positions, and verify the chosen rule across the full sequence.
Key points
- Start with first differences, then test ratios or second differences.
- Separate odd and even positions when a sequence alternates.
- Convert letters to positions only when it clarifies the rule.
- A valid rule should explain every transition shown.