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Sequences definitions

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  • Sequence
    An ordered list of numbers where each entry follows a specific pattern or rule, often described by a formula.
  • Term
    An individual number or element in an ordered list, identified by its position within the sequence.
  • Index
    A positive integer indicating the position of a term within an ordered list, typically represented by n.
  • Finite Sequence
    An ordered list of numbers with a definite end, containing a specific number of terms.
  • Infinite Sequence
    An ordered list of numbers that continues indefinitely without a final term, often denoted with ellipsis.
  • Explicit Formula
    An equation involving n that allows direct calculation of any term in an ordered list without reference to previous terms.
  • Recursive Formula
    A rule that defines each term in an ordered list based on one or more preceding terms, requiring initial values.
  • Arithmetic Sequence
    An ordered list where each term increases or decreases by a constant value, forming a linear pattern.
  • Exponential Sequence
    An ordered list where each term is a constant raised to the power of the index, resulting in rapid growth or decay.
  • Fractional Sequence
    An ordered list where terms are fractions, often with numerators and denominators following distinct patterns.
  • Pattern
    A recognizable regularity or rule that determines the progression of terms in an ordered list.
  • Subscript Notation
    A way to label terms in an ordered list using a variable with a subscript, such as aₙ, to indicate position.
  • Alternating Sequence
    An ordered list where the sign or value of terms alternates in a regular fashion, often involving powers of negative one.
  • General Formula
    A mathematical expression that provides a direct method to compute any term in an ordered list based on its position.
  • Function
    A mathematical relationship similar to an ordered list, but with inputs that can be any real number, not just positive integers.