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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 constant factor.
  • Arithmetic Sequence
    A list of numbers where each term is found by adding a constant value to the previous term.
  • Common Ratio
    The fixed number by which each term in a geometric sequence is multiplied to get the next term.
  • Recursive Formula
    An equation that defines each term of a sequence using the previous term and a specific operation.
  • General Formula
    An equation that allows direct calculation of any term in a sequence using its position, the first term, and a constant.
  • Exponential Growth
    A pattern where values increase rapidly due to repeated multiplication by a constant factor.
  • First Term
    The initial value from which a sequence begins and which is essential for constructing formulas.
  • Index
    A number indicating the position of a term within a sequence.
  • Term
    An individual element or value in a sequence, identified by its position.
  • Sequence
    An ordered list of numbers following a specific pattern or rule.
  • Power
    The exponent to which a number is raised, often used in general formulas for geometric sequences.
  • Constant Difference
    A fixed value added between terms in an arithmetic sequence.
  • Constant Ratio
    A fixed value multiplied between terms in a geometric sequence.
  • Nth Term
    A term located at the n-th position in a sequence, often found using a general formula.
  • Multiplication
    The operation used to progress from one term to the next in a geometric sequence.