1. Graphing Sequences
Section 1.4

2. There is more than one way to represent a sequence.
Tables
Graphs
Other kinds of formulas

3. Match each table with a recursive formula and a graph that represent the same sequence. Think about similarities and differences between the sequences and how those similarities and differences affect the tables, formulas, and graphs.
Write a paragraph that summarizes the relationships between different types of
sequences, recursive formulas, and graphs. What generalizations can you make?
What do you notice about the shapes of the graphs created from arithmetic and
geometric sequences?

4. Setting Up a Spreadsheet with a Sequence
Open a new document and start with a List and Spreadsheet.
Label column A xcoord
Label column B ycoord
Fill the first two cells in column A with1 and 2. Press the Caps key and the down arrow to highlight the two cells. Press MENU, choose DATA, choose Fill. Cursor down to highlight the first 10 cells and press ENTER.

5. Move to the box under ycoord to enter a command to make a sequence.
Press Menu, 3 Data, 1 Generate Sequence. Fill in the formula for the sequence, the initial terms, n(), nMax.

6. To create a graph of the data in your spreadsheet, press HOME, add a Data and Statistics page.
Move to the edge with the cursor and select xcoord for the bottom axis and ycoord for the vertical axis

7. This is an arithmetic sequence
The general shape of the graph of a sequence’s terms tells you about the type of sequence you have generated.
This is an arithmetic sequence

8. This is a geometric sequence.
The general shape of the graph of a sequence’s terms tells you about the type of sequence you have generated.
This is a geometric sequence.

9. Example
In deep water, divers find that their surroundings become darker the deeper they go. The data here give the percent of surface light intensity that remains at depth n ft in a particular body of water.
Depth (ft) 10 20 30 40 50 60 70
Percent of surface light
100 78 47 36 28 22 17
A graph of the data shows a decreasing, curved pattern. It is not linear, so an
arithmetic sequence is not a good model. A geometric sequence with a long-run value of 0 will be a better choice.

10. Check this model by graphing the original data and the sequence on your calculator.
The graph shows that this model fits only one data point—it does not decay fast enough.

11. Experiment by increasing the rate of decay
Experiment by increasing the rate of decay. With some trial and error, you can find a model that fits the data better.