This week in math 10 I learned about the different sequences and how they are classified. The three main types of sequences are arithmetic sequences, which are the ones we are focusing on most in this unit, then the geometric sequences, and then any other sequences that do not fall into either of those categories. Within each of these sequences they can be either finite which is when the sequence has an end or will eventually stop or they can be infinite, when they do not have a stop and that is represented by … at the end of a sequence.

**Arithmetic Sequences **

Arithmetic sequences are when the pattern or common difference of the sequence is the same number adding or subtracting to each term.

Example:

**Geometric Sequences**

Geometric sequences are when the sequence is multiplied by the same number to each term.

Example:

**Other Sequences**

The other sequences is any thing that is not a geometric or arithmetic sequences.

Example:

The pattern in the example is the two numbers in front are added to get the next number.

You can also take these sequences and put them into a chart by putting the sequence into the y and the number of each term in the x column. If the sequence is arithmetic the common difference of the sequence (the number that is added or subtracted from each term) when you graph it you will notice that it is the same as the slope of the line.

If the table is

X Y

1 2

2 4

3 6

4 8

5 10

The common difference between the y values is 2 on the table and if you look at the graph below you can see that the slope of the line is 2.