Learn Before
Examples: Determining if a Sequence Is Arithmetic and Finding the Common Difference
Determine whether each sequence is arithmetic and, if so, state the common difference.
-
5, 9, 13, 17, 21, 25, dots Subtract consecutive terms: , , , , . Every difference equals , so the sequence is arithmetic with .
-
4, 9, 12, 17, 20, 25, dots 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 .
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.12 Sequences, Series and Binomial Theorem - Intermediate Algebra @ OpenStax
Algebra
Related
General Term of an Arithmetic Sequence
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.
A department manager is tracking a steady, constant reduction in monthly operational expenses. In this scenario, which of the following must be true about the constant value known as the common difference ()?
A department manager is reviewing a monthly budget that increases by a fixed amount of 125 dollars every month. In the arithmetic sequence representing these budget totals, the constant value of 125 is formally known as the ____.
A financial auditor is reviewing a series of monthly payments that form an arithmetic sequence. To identify the common difference (), the auditor must follow the formal mathematical definition. Arrange the following steps in the correct order to calculate and verify the common difference.
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.
Defining the Constant Rate of Change in Sales Data
Training Team Members on Tracking Consistent Operational Trends
Examples: Determining if a Sequence Is Arithmetic and Finding the Common Difference
Learn After
A part-time employee tracks their daily tips for a week. The amounts earned (in dollars) are: {}4, 9, 12, 17, 20, 25. 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.
A warehouse supervisor tracks the stock of a specific part, which decreases by the same amount each week: {}1000, 950, 900, 850. Because the difference between any two consecutive weeks is a constant value of -50, this pattern of values is classified as a(n) ____ sequence.
True or False: A quality control technician monitors the daily output of a production line and records the following values over five days: {}12, 18, 24, 31, 38. This sequence is classified as arithmetic because the daily output is consistently increasing.
A logistics manager is reviewing a series of cargo weights to determine if the progression follows an arithmetic pattern: {}40, 45, 50, 55, 60 tons. Arrange the following steps in the correct order to verify if this data set represents an arithmetic sequence.
Verifying Arithmetic Patterns in Weekly Sales Data
Verifying Arithmetic Patterns in Daily Stock Levels