- Topics At a Glance
- Sequences
- Defining Sequences and Evaluating Terms
- Patterns
- Sequences Can Start at
*n*= 0 - Special Types of Sequences
- Arithmetic Sequences
- Geometric Sequences
- Comparing Arithmetic and Geometric Sequences
**Visualizing Sequences****2-D Graphs**- Convergence and Divergence of Sequences
- Other Useful Sequence Words
- Heads and Tails
- Word Problems
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

We have all had sliced bread. It's been around since 1928. Two-dimensional graphs have been around for a while, too. While number lines are nice, we can't tell which dots go with which terms. Since we as much about 2-D graphs as we do sliced bread, we may as well use them and see what happens.

To graph a sequence on a 2-D graph, we put *n* on the horizontal axis and *a _{n}* on the vertical axis.

For each term *a _{n}* of the sequence we graph the point (

Plot the first five terms of the sequence , starting at *n* = 1, on a graph.

Answer.

We plot the points

to get this graph:

Even though the terms flip back and forth like a floundering fish, we can see that the values *a _{n}* get closer to 0 as

After going through this example, you don't need your fortune-telling turban or crystal ball to see we are heading for limits of sequences. Back the bus up for a second. First, we should go through a couple exercises to see a few more sequences plotted in two dimensions.

Exercise 1

Plot the first five terms of the sequence on a 2-D graph.

*a _{n}* = 2

Exercise 2

Plot the first five terms of the sequence on a 2-D graph.

*a _{n}* = (-1)

Exercise 3

Plot the first five terms of the sequence on a 2-D graph.