This week in math I learned about infinite geometric sequences, series, and their respective formulas and graphing. There are two different kinds of infinite geometric sequences and series: converging and diverging.

For a diverging geometric series, the sum is infinite, and thus the graph will constantly grow. No matter the numbers, any diverging series has a ratio greater than 1 or less than -1, and will always have no sum. Graphs for diverging series’ look like this:

For a converging geometric series, the sum is . The ratio must always be less than 1 and greater than -1, and because of this, the graph will always get smaller, with the sum being finite. This is a graph for a converging series:

This week in math, I learned of the usefulness of graphs for checking arithmetic or geometric sequences. You can easily identify if a sequence is geometric, arithmetic, or neither with a simple graph.

An arithmetic sequence will always be a simple linear graph, meaning it will appear as a straight line.

A geometric sequence will always consist of a curved graph, with the distance between each term on the graph increasing each time. This is a bit harder to identify, but can still be helpful.

So, I learned if you are ever positively unsure about a sequence, put it into a graph, and can get easy results.