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 an 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 an = 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.
an = 2n
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.
an = (-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.
