Graphing an arithmetic sequence involves plotting the terms of the sequence on a coordinate plane. Here’s a step-by-step guide to help you graph an arithmetic sequence:
- Identify the Sequence: First, identify the arithmetic sequence you want to graph. An arithmetic sequence is defined by its first term and the common difference between consecutive terms. For example, consider the sequence: 2, 5, 8, 11, 14, …
- Determine the Terms: List out the terms of the sequence. In our example, the terms are 2, 5, 8, 11, 14, …
- Assign Positions: Assign each term a position number (n). The first term is position 1, the second term is position 2, and so on. For our example:
- Position 1: 2
- Position 2: 5
- Position 3: 8
- Position 4: 11
- Position 5: 14
- Plot the Points: On a coordinate plane, plot the points where the x-coordinate is the position number (n) and the y-coordinate is the term value. For our example, the points to plot are:
- (1, 2)
- (2, 5)
- (3, 8)
- (4, 11)
- (5, 14)
- Connect the Dots: Once all the points are plotted, connect them with a straight line. This line represents the arithmetic sequence.
By following these steps, you can easily graph any arithmetic sequence. Remember that the graph of an arithmetic sequence will always be a straight line because the difference between consecutive terms is constant.