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Arithmetic Sequences definitions

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  • Arithmetic Sequence
    A list of numbers where each term increases or decreases by the same fixed amount between consecutive terms.
  • Common Difference
    The fixed value added or subtracted between any two consecutive terms, often represented by the letter d.
  • General Term
    A formula that allows calculation of any term in the sequence using its position, the first term, and the common difference.
  • First Term
    The initial value in the sequence, often labeled as a1, which serves as the starting point for calculations.
  • Consecutive Terms
    Two terms that appear one after the other in the sequence, used to determine the common difference.
  • Index
    The position number of a term in the sequence, usually denoted by n, indicating which term is being referenced.
  • Formula
    An algebraic expression used to find specific terms or properties of the sequence, such as an=a1+(n-1)×d.
  • Pattern
    A recognizable regularity in the sequence, often based on the repeated addition or subtraction of the common difference.
  • Sequence
    An ordered list of numbers arranged according to a specific rule or relationship.
  • Term
    An individual value in the sequence, identified by its position and calculated using the general term formula.
  • Variable
    A symbol, often n or d, used in formulas to represent unknown or changing values within the sequence.
  • Simplification
    The process of rewriting a formula or expression in a more concise or manageable form, such as combining constants.
  • Negative Common Difference
    A situation where the fixed value between terms is less than zero, causing the sequence to decrease.
  • Algebra
    A branch of mathematics used to manipulate formulas and solve for unknowns within the sequence context.
  • Nth Term
    The value at a specific position in the sequence, calculated using the general term formula and the index n.