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Geometric Sequences definitions

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  • Geometric Sequence
    A list of numbers where each term is found by multiplying the previous term by a fixed, nonzero value.
  • Arithmetic Sequence
    A list of numbers where each term is found by adding a constant value to the previous term.
  • Common Ratio
    A fixed value by which each term in a geometric sequence is multiplied to get the next term.
  • Common Difference
    A fixed value added to each term in an arithmetic sequence to obtain the next term.
  • Recursive Formula
    An equation that defines each term of a sequence using the previous term and a constant value.
  • General Formula
    An equation that allows direct calculation of any term in a sequence without reference to previous terms.
  • First Term
    The initial value from which a sequence begins, often denoted as A₁.
  • Exponential Growth
    A pattern where values increase rapidly due to repeated multiplication by a constant factor.
  • Index
    A position number assigned to each term in a sequence, usually represented by n.
  • Nth Term
    A general term representing the value at position n in a sequence, often denoted as Aₙ.
  • Power
    An expression indicating how many times a number, the base, is multiplied by itself.
  • Sequence
    An ordered list of numbers following a specific pattern or rule.
  • Term
    An individual element or value in a sequence.
  • Pattern
    A repeated or regular way in which numbers in a sequence are arranged.
  • Multiplication
    The mathematical operation used to progress from one term to the next in a geometric sequence.