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Common Difference of an Arithmetic Sequence
The common difference of an arithmetic sequence, denoted by , is the constant value obtained when any term is subtracted from the term that directly follows it. Formally, for every integer . The common difference can be positive, negative, or zero. When the terms increase (e.g., has ); when the terms decrease (e.g., has ); and when every term is identical. To verify that a sequence is arithmetic, compute the difference between each pair of consecutive terms: if all differences equal the same value, that value is .
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Ch.12 Sequences, Series and Binomial Theorem - Intermediate Algebra @ OpenStax
Algebra
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In operational tracking, such as projecting steady monthly inventory growth or predicting regular budget decreases, identifying the mathematical pattern is critical. In an arithmetic sequence, this constant change is governed by the common difference (). Match each characteristic of the common difference to its correct effect or definition.
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A sales manager is analyzing a quarterly report where the number of new client acquisitions forms an arithmetic sequence. To determine the common difference (), the manager must subtract any quarter's number of acquisitions from the number of acquisitions in the quarter that directly preceded it.