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
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.