Study the expanded notes and the credited detailed textbook lessons. The current chapter index covers core topics; it is not a claim of exhaustive coverage of every examination syllabus. Check the official syllabus and primary references.
Series and Patterns — lesson overview
Numerical patterns
A number series can involve differences, ratios, alternating subsequences or combinations. Inspect changes before choosing a rule.
For 2, 5, 10, 17, differences are 3, 5 and 7; continuing the odd-difference pattern gives the next term 26.
A finite sequence can fit many mathematical rules. Aptitude answers depend on the intended simple pattern and the available options or instructions.
Alphabetical and mixed series
Letter series can use alphabet positions, alternating directions or fixed shifts. Track each subsequence separately where the pattern alternates.
Mixed letter–number series may contain independent components; establish whether the components interact before combining them.
Boundary conventions such as wrapping after Z must be consistent with the question rather than assumed without checking.
Error detection
For a proposed wrong-term problem, test whether replacing one term restores a consistent pattern across all transitions.
Do not invent a different rule for every pair merely to preserve a preferred answer. The explanatory rule should be compact and consistent.
Compute intermediate differences carefully; arithmetic slips can look like a failure of the underlying pattern.
Check several simple representations of a sequence
Begin with first differences, then ratios, alternating subsequences, and familiar powers where appropriate. For 3, 7, 13, 21, 31, the first differences are 4, 6, 8, 10; continuing the difference pattern gives 12 and the next term 43. The second differences are constant at 2, suggesting a quadratic pattern in the index rather than a constant multiplication.
For 2, 6, 18, 54, a ratio of 3 consistently connects terms, so the next term is 162 under that simple rule. For 2, 10, 4, 20, 6, 30, separating odd and even positions reveals 2,4,6 and 10,20,30. Failing to separate alternating structures can tempt the solver into an unnecessarily complicated recurrence.
A pattern must be checked against every step, including the beginning. A rule that fits only the final pair is weak evidence. Also distinguish a missing internal term from a next-term question: a candidate filling the gap must satisfy both the transition before and after it, giving more constraints than a one-sided extrapolation.
A likely examination pattern is not a proof of uniqueness
Any finite set of terms can be extended by many mathematical rules. In an examination the intended answer is generally the simple regularity supported by the question and options. This is a convention of puzzle design, not a theorem that a finite sequence determines all later values uniquely.
For a wrong-number problem, compute the relevant differences or ratios around each candidate. Replacing a term should restore one consistent structure rather than repair one local step while breaking another. For alphabet series, convert to positions only when useful, and check wrap-around and alternating directions explicitly.
Use estimation to reject unreasonable answers: a steady positive multiplication suggests rapid growth, whereas increasing small differences suggest a slower pattern. Do not treat every unusual term as a typo or invent a high-degree polynomial merely to force one option. The strongest solution states the rule, demonstrates its consistency, performs the arithmetic, and recognises any genuine ambiguity.
