Find the changing rule in Number Series and predict the next value.
What this question type measures
Number Series measure pattern recognition, working memory, and flexible use of operations when a sequence follows one rule or an alternating set of rules.
How to solve it
- Study every part of the prompt before looking at the choices.
- Name the relationship, rule, or change in simple words.
- Apply that same rule to the unanswered part.
- Eliminate choices that satisfy only part of the rule, then check the best answer.
Original practice example
2, 5, 8, 11, ___.
Reasoning: Each term increases by 3, so the next number is 14.
Practice tips
- Ask the learner to explain the rule aloud before selecting an answer.
- Compare close distractors and identify exactly where each one breaks the rule.
- Practice accurately first; add timing only after the process is understood.
This is an original CogAT.org learning example. It is not an official or recalled test item.
How CogAT Number Series questions work
Number Series questions ask for the value that continues a numerical pattern. Some use a constant change, while others alternate operations, increase the size of the change, or interleave two simpler sequences. The correct rule must account for every transition shown.
Reasoning skills involved
- Comparing consecutive terms and recording the differences
- Recognizing repeated multiplication or division
- Separating alternating or interleaved sequences
- Testing a rule across the entire series rather than the final pair
A repeatable solving method
- Calculate the change between each pair of neighboring terms.
- Look for a repeated change before testing a more complex rule.
- If changes alternate, separate odd-position and even-position terms.
- Apply the verified next step once and check its scale for reasonableness.
Common mistakes to avoid
- Guessing from the last two numbers only
- Forcing one operation when the pattern alternates
- Continuing a difference pattern without checking earlier terms
How to practice productively
Begin untimed and ask the learner to explain the rule or clue before choosing an answer. Review why each close distractor fails. Add short timed sets only after the method is accurate and familiar. This approach builds transferable reasoning instead of memorizing answers.
Independent educational resource: CogAT.org is not affiliated with or endorsed by the test publisher. Examples and practice materials are original and are not copied, recalled or secure test questions. Schools determine the assessment level, administration and use of results.