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Geometric Sequences definitions

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  • Geometric Sequence
    A list of numbers where each term is obtained by multiplying the previous term by a fixed value called the common ratio.
  • Arithmetic Sequence
    A list of numbers where each term is obtained by adding a fixed value called the common difference to the previous term.
  • Common Ratio
    A constant multiplier used to generate each term from the previous term in a geometric sequence.
  • Common Difference
    A constant value added to each term to produce the next term in an arithmetic sequence.
  • Term
    An individual value or number in a sequence, identified by its position.
  • First Term
    The initial value in a sequence, often used as a starting point for formulas.
  • General Term
    A formula that expresses any term in a sequence based on its position and sequence parameters.
  • Position
    The place or index of a term within a sequence, often denoted by n.
  • Exponent
    A mathematical notation indicating how many times a number, such as the common ratio, is multiplied by itself.
  • Formula
    A mathematical expression used to calculate terms in a sequence efficiently.
  • Sequence
    An ordered list of numbers following a specific pattern or rule.
  • Fraction
    A numerical value expressed as a ratio of two integers, often appearing in sequence terms.
  • Multiplier
    A value by which another number is multiplied, such as the common ratio in geometric sequences.
  • Pattern
    A repeated or predictable arrangement of numbers in a sequence.
  • Series
    A sum of terms from a sequence, often used in advanced algebra topics.
  • Index
    A numerical label for the position of a term in a sequence, usually represented by n.
  • Power
    The result of raising a number, such as the common ratio, to an exponent in sequence formulas.
  • Practice Problem
    An exercise designed to reinforce understanding of sequence concepts and formulas.
  • Numerator
    The top part of a fraction, representing the number of parts considered.
  • Denominator
    The bottom part of a fraction, representing the total number of equal parts.
  • Simplification
    The process of reducing a mathematical expression, such as a fraction, to its simplest form.
  • Constant
    A fixed value that does not change within the context of a sequence.
  • Value
    The numerical amount assigned to a term in a sequence.
  • Zero Power
    A mathematical concept where any number raised to the zero exponent equals one.
  • Product
    The result of multiplying numbers, such as terms in a geometric sequence.
  • Division
    A mathematical operation used to find the common ratio by comparing consecutive terms.
  • Calculation
    The process of determining the value of a term using sequence formulas.
  • Expression
    A combination of numbers and symbols representing a mathematical relationship in sequences.
  • Nth Term
    A term located at position n in a sequence, calculated using the general term formula.