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Introduction to Sequences definitions

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  • Sequence
    A list of numbers arranged in a specific order, each associated with a positive integer index.
  • Domain
    The set of positive integers used as input values for generating terms in a sequence.
  • Index
    A positive integer that identifies the position of a term within a sequence.
  • Term
    A value in a sequence corresponding to a specific index, often denoted with a subscript.
  • General Term
    An expression involving the index that produces any term in a sequence when substituted.
  • Explicit Formula
    An equation that directly relates the index to the value of each term in a sequence.
  • Finite Sequence
    A sequence with a limited number of terms, ending at a specific index.
  • Infinite Sequence
    A sequence that continues indefinitely without a final term.
  • Arithmetic Progression
    A sequence where each term increases or decreases by a constant difference.
  • Exponential Sequence
    A sequence where each term is a constant base raised to the index, causing rapid growth.
  • Alternating Sequence
    A sequence in which the sign of each term switches between positive and negative.
  • Fractional Sequence
    A sequence where each term is a fraction, often with numerators and denominators following patterns.
  • Subscript Notation
    A way to label terms in a sequence using the index as a small number beside the variable.
  • Pattern
    A recognizable regularity in the arrangement or values of terms within a sequence.
  • Constant
    A fixed value used to adjust formulas for sequences, ensuring correct starting points or differences.