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Sequences definitions

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  • Sequence
    An ordered list of numbers where position matters and each entry follows a specific pattern or rule.
  • Term
    An individual number or element in an ordered list, often labeled with a subscript to indicate its position.
  • Index
    A positive integer indicating the position of an entry in an ordered list, typically represented by n.
  • Finite Sequence
    An ordered list of numbers with a definite end, containing a limited number of entries.
  • Infinite Sequence
    An ordered list of numbers that continues without end, often indicated by ellipsis.
  • General Formula
    An equation involving the position variable that directly calculates any entry in an ordered list.
  • Recursive Formula
    An equation that determines each entry based on one or more previous entries in the ordered list.
  • Arithmetic Sequence
    An ordered list where the difference between consecutive entries remains constant throughout.
  • Common Difference
    A fixed value added or subtracted to move from one entry to the next in an arithmetic pattern.
  • Geometric Sequence
    An ordered list where each entry is obtained by multiplying the previous entry by a fixed value.
  • Common Ratio
    A fixed multiplier used to progress from one entry to the next in a geometric pattern.
  • Explicit Formula
    An equation that provides a direct calculation for any entry in an ordered list, synonymous with general formula.
  • Subscript Notation
    A labeling method using small numbers to indicate the position of entries in an ordered list.
  • Pattern
    A recognizable regularity or rule that governs the progression of entries in an ordered list.
  • Output
    A value produced by applying a rule or formula to a specific position in an ordered list.