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
The first five terms are 2, 4, 8, 16, and 32.
As n gets larger, the terms increase, getting farther apart from each other.
an = (-1)n
The first five terms are -1, 1, -1, 1, -1. When we plot these on a number line we only see two dots:
The terms bounce back and forth between 1 and -1 forever.
The first five terms are 5, 4.5, 4.333..., 4.25, 4.2.
The terms are getting closer to 4.
Make it rain.