# Sequences

### Topics

## Introduction to Sequences - At A Glance:

For those who like pictures better than formulas, we can visualize sequences on number lines and on graphs. For those who like Kit Kats, we can visualize a giant Kit Kat bar. Either way, creating an image will help us understand better how some sequences behave.

## Numberlines

Some sequences are well-behaved like well-trained dogs, while others are as unpredictable as wild tigers. If we plot the terms of a sequence on a number line, we can get some intuition for what the terms of the sequence are doing.

### Sample Problem

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

Answer.

The first five terms are

Plotting these on a number line, we get

We can see that as *n* gets larger, the terms of the sequence are clumping around 0.

Even if we don't label the terms *a _{n}* on the number line, we can still tell something about what the sequence is doing.

#### Example 1

Plot the first five terms of the sequence n, starting at n = 1, on a number line. |

#### Exercise 1

Plot the first five terms of the sequence on a number line (start with *n* = 1). Describe in words how the terms are behaving as *n* gets larger.

*a _{n}* = 2

^{n}#### Exercise 2

Plot the first five terms of the sequence on a number line (start with *n* = 1). Describe in words how the terms are behaving as *n* gets larger.

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

^{n}#### Exercise 3

Plot the first five terms of the sequence on a number line (start with *n* = 1). Describe in words how the terms are behaving as *n* gets larger.