Pattern Recognition — Fundamental Concepts

Fundamental Concepts

Find a rule, then test it

Pattern recognition means identifying a consistent relationship in the information supplied. In an aptitude question, the strongest candidate rule explains the given terms with a simple, repeatable operation. A finite sequence can admit many mathematical continuations, so the wording and answer options matter: do not mistake a guessed rule for a unique theorem.

Inspect the right feature

For numbers, try differences, ratios, alternating subsequences and squares or cubes. For letters, translate positions using A = 1 through Z = 26 and state any wrap-around convention. For figures, track rotation, reflection, number of elements and shading independently before combining them. A change in one feature does not imply that every feature changes at the same rate.

Work a complete example

Consider 4, 9, 16, 25, 36 under the rule of consecutive integer squares. The terms are 2², 3², 4², 5² and 6², so the next is 7² = 49. The differences 5, 7, 9 and 11 provide a second check: the next difference is 13. Simply repeating the last difference gives 47, which fits the latest step but breaks the earlier progression.

For an alternating series, label odd and even positions before calculating. In 3, 20, 6, 18, 9, 16, the odd-position terms rise by 3 and the even-position terms fall by 2. The seventh term is therefore 12 under that rule, not 14 from extending the even branch.

Verify before choosing

Write the proposed rule in one sentence, apply it to each supplied transition, and eliminate options that require an unexplained exception. This makes the method reproducible and exposes arithmetic slips.