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Example: Determining if a Sequence Is Arithmetic
Determine whether each sequence is arithmetic and, if so, state the common difference.
ⓐ
Subtract consecutive terms: , , , , . Every difference equals , so the sequence is arithmetic with .
ⓑ
Subtract consecutive terms: , , , , . The differences alternate between and , so the sequence is not arithmetic and has no common difference.
ⓒ
Subtract consecutive terms: , , , , . Every difference equals , so the sequence is arithmetic with .
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Intermediate Algebra @ OpenStax
Ch.12 Sequences, Series and Binomial Theorem - Intermediate Algebra @ OpenStax
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Example: Determining if a Sequence Is Arithmetic
General Term of an Arithmetic Sequence
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A part-time employee tracks their daily tips for a week. The amounts earned (in dollars) are: . To determine if this sequence is arithmetic, the employee calculates the differences between consecutive days. Based on the definition of an arithmetic sequence, which statement is true?
A manufacturing plant supervisor is analyzing different production and quality metrics over several shifts. Match each sequence of recorded values to its correct mathematical classification based on whether it represents an arithmetic sequence and what its common difference is.
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A logistics manager is reviewing a series of cargo weights to determine if the progression follows an arithmetic pattern: tons. Arrange the following steps in the correct order to verify if this data set represents an arithmetic sequence.