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Arithmetic Sequences definitions

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  • Arithmetic Sequence
    A list of numbers where the difference between consecutive terms remains constant throughout.
  • Common Difference
    The fixed value added or subtracted between consecutive terms in an arithmetic sequence, often denoted as d.
  • Recursive Formula
    An equation that defines each term of a sequence using the previous term and the common difference.
  • General Formula
    An explicit equation that allows direct calculation of any term in a sequence using its position, the first term, and the common difference.
  • First Term
    The initial value from which an arithmetic sequence begins, often denoted as a₁.
  • Nth Term
    A specific term in a sequence identified by its position, calculated using the general formula.
  • Index
    A number indicating the position of a term within a sequence, typically represented by n.
  • Consecutive Terms
    Two terms that appear one after the other in a sequence.
  • Positive Common Difference
    A situation where each term in the sequence increases by a fixed amount.
  • Negative Common Difference
    A situation where each term in the sequence decreases by a fixed amount.
  • Explicit Formula
    Another name for the general formula, providing a direct way to find any term without previous terms.
  • Sequence
    An ordered list of numbers following a specific pattern or rule.
  • Term
    An individual number or element within a sequence.
  • Pattern
    A recognizable regularity or rule that defines the progression of terms in a sequence.
  • Subscript Notation
    A way to label terms in a sequence using indices, such as a₁, a₂, a₃, etc.