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Sequences definitions

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  • Sequence
    An ordered list of numbers, either finite or infinite, where each number is called a term and follows a specific pattern.
  • Term
    An individual number in a sequence, identified by its position and often generated by a formula or pattern.
  • Index
    A positive integer representing the position of a term within a sequence, typically denoted by n.
  • Finite Sequence
    A sequence with a limited number of terms, ending at a specific value without continuing indefinitely.
  • Infinite Sequence
    A sequence that continues without end, often indicated by an ellipsis after the last visible term.
  • Pattern
    A recognizable regularity or rule that determines how terms in a sequence are generated or related.
  • General Formula
    An explicit equation involving the index n, used to calculate any term in a sequence directly.
  • Recursive Formula
    An equation that defines each term of a sequence based on one or more previous terms, requiring initial values.
  • Arithmetic Sequence
    A sequence where each term increases or decreases by a constant difference from the previous term.
  • Explicit Formula
    A synonym for general formula, providing a direct calculation for any term using the index.
  • Subscript Notation
    A way to label terms in a sequence, such as a₁, a₂, a₃, indicating their position using subscripts.
  • Fraction Sequence
    A sequence where terms are fractions, often with numerators and denominators following their own patterns.
  • Exponential Sequence
    A sequence where each term is generated by raising a base number to the power of the index or a related expression.
  • Alternating Sequence
    A sequence in which the sign or value of terms alternates, often modeled using powers of negative one.
  • Function
    A mathematical relationship similar to a sequence, but with inputs that can be any real number, not just positive integers.