Final answer:
The arithmetic sequence is graphed by plotting each term on a coordinate plane with the x-axis as the term number and the y-axis as the term value, and connecting the points to show the pattern. A dot plot or histogram represents different data types by placing dots or bars at intervals respectively.
Step-by-step explanation:
To graph the arithmetic sequence 6, 5.25, 4.5, 3.75, ..., we first recognize that this sequence is decreasing by a common difference of 0.75. Graphing this sequence involves plotting the terms of the sequence on a coordinate plane. Here's how to graph the sequence:
- Set up a coordinate plane with the x-axis representing the term number (n) and the y-axis representing the term value.
- Label the x-axis with consecutive integers starting from 1, as each integer will represent the term number in the sequence.
- Label the y-axis with values that include the terms of the sequence. In this case, it should at least range from 3.75 to 6.
- Plot the first term at (1, 6), the second term at (2, 5.25), and so on, decreasing by 0.75 each time.
- Connect the points with a straight line to emphasize the decreasing nature of the arithmetical pattern.
To compare, a dot plot or a histogram could be used to represent other types of data. For example, in creating a dot plot, you would place dots above a number line at the values corresponding to the data points. Similarly, constructing a histogram entails creating bars to represent the frequency of data in specified intervals.