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# Sequences

# 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 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 (

*n*,

*a*).

_{n}### 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 *a _{n}* 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 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.