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Common Ratio of a Geometric Sequence
The common ratio of a geometric sequence, denoted by , is the constant value obtained when any term is divided by the term immediately before it. Formally, for every integer . To verify that a sequence is geometric, compute the ratio between each pair of consecutive terms: if all ratios are the same value, that value is and the sequence is geometric. If even one ratio differs from the others, the sequence is not geometric and no common ratio exists. The common ratio can be any nonzero number — positive, negative, a whole number, or a fraction.
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Intermediate Algebra @ OpenStax
Ch.12 Sequences, Series and Binomial Theorem - Intermediate Algebra @ OpenStax
Algebra
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Example: Determining if a Sequence Is Geometric
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A retail analyst is studying the monthly sales growth of a new store and determines that the sales figures follow a geometric sequence. To identify the common ratio () of this growth pattern, which of the following definitions must the analyst use?
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