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# At a Glance - 2-D Graphs

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 know 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 an on the vertical axis.

For each term an of the sequence we graph the point (n, an).

### Sample Problem

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 an get closer to 0 as n gets larger.

After going through this example, you don't need your fortune-telling turban or crystal ball to see we're 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.

an = 2n

#### Exercise 2

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

an = (-1)n

#### Exercise 3

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