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Introduction to Sequences definitions

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  • Sequence
    A function mapping positive integers to numbers, forming a list that can model patterns and predict values.
  • Domain
    The set of positive integers used as input values for generating terms in a sequence.
  • Index
    A positive integer representing the position of a term within a sequence, often denoted by n.
  • Term
    An output value in a sequence, determined by substituting the index into the general formula.
  • General Term
    An expression involving the index that defines how each term in a sequence is calculated.
  • Explicit Formula
    An equation that directly relates the index to the value of each term in a sequence.
  • Finite Sequence
    A list of terms with a limited number of values, ending at a specific index.
  • Infinite Sequence
    A list of terms that continues indefinitely, with no upper bound on the index.
  • Arithmetic Progression
    A sequence where each term increases or decreases by a constant difference from the previous term.
  • Geometric Progression
    A sequence where each term is obtained by multiplying the previous term by a constant factor.
  • Exponent
    A mathematical notation indicating repeated multiplication, often used in geometric sequences.
  • Numerical Coefficient
    A constant multiplied by the index or other expressions in the general term of a sequence.
  • Alternating Sign
    A pattern in a sequence where the sign of each term switches between positive and negative.
  • Fraction
    A term in a sequence expressed as a ratio of two numbers, often involving patterns in numerator and denominator.
  • Pattern
    A recognizable regularity in the arrangement of terms within a sequence, guiding formula creation.