Writing+Linear+Functions-Target+E-Arithmetic+Sequence-Guided+Learning

**Writing Linear Functions-Target E: Determine Whether a Set of Data Represents an Arithmetic Sequence**

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An arithmetic sequence can be represented by a set of numbers that either increase or decrease by a constant value. Examples of an arithmetic sequence are given by the following:

Set C: 2, 8, 14, 20, 26, 32,…

Set D: 34, 26, 18, 10, 2, -6, …

Set C represents an arithmetic sequence because each number in the set is being increased by 6 to get to the next number. Set D represents an @arithmetic sequence because each number in the set is being decreased by 8 to get to the following number.

We can use this information to help determine whether or not a set of data represents a linear relationship. Using the tables below, look at how the x-values and y-values change. If the values in the table increase or decrease by a constant value, then the relationship is linear. This means that if you were to graph the set of points represented in the table, they could connect to form a straight line, because they are increasing or decreasing by a constant rate of change.

The set of data points from Table A represents a linear relationship because both the x-values and y-values are increasing by a constant value. If you look at the graph to the right, the points follow the pattern of a line. The set of data points from Table B do not represent a linear relationship becuase although the x-values are increasing by a constant value, the y-values are not. Also, if you look at the graph of the points, they do not follow the pattern of a lne.

Do the following sets of numbers represent an arithmetic sequence? math 1)\space\space\ \text{-}3, \text{-}4, 13, 23, \text{-}24 math
 * Writing Linear Functions-Target E-Arithmetic Sequence-Quick Check:**

math 2)\space\space\large\frac{5}{6}, \frac{1}{3}, \text{-}\frac{1}{6}, \text{-}\frac{2}{3}, \text{-}\frac{7}{6}\ math

Does the table represent a linear relationship? media type="custom" key="26597176"

Writing Linear Functions-Target E-Arithmetic Sequence-Quick Check Solutions