Glossary term · Calculus reference

Sequence: Meaning, Notation, and Example

An ordered list whose terms are indexed.

Definition and meaning

Order and repetition matter in a sequence. A formula or recurrence may define its terms.

The term sequence names a precise mathematical idea, not merely a visual pattern. Read its notation as a statement with hypotheses, quantities, and a conclusion.

Notation

a1,a2,a3,a_1,a_2,a_3,\ldots

Read every symbol with its domain and hypotheses; notation compresses an argument but does not remove its conditions.

Worked example

Identify the quantities in the notation, state the relevant hypothesis, and explain what conclusion the sequence statement permits.

Common confusion

Do not treat sequence as a keyword that automatically selects a formula; its hypotheses and domain still control the conclusion.

Revised 2026-07-23. Original BetterGrades material. Free classroom and personal study use with attribution; no resale.