Definition Numerical Sequence
A numerical sequence is a list of numbers that follows a specific rule.
- The first number is called the 1\(^{\text{st}}\) term.
- The second number is called the 2\(^{\text{nd}}\) term.
- The third number is called the 3\(^{\text{rd}}\) term.
- And so on.
Example
What is the 6\(^{\text{th}}\) term of this sequence?
| \(n\) | 1 | 2 | 3 | 4 | 5 | 6 |
| \(n^{\text{th}}\) term | 3 | 5 | 7 | 9 | 11 | 13 |
The 6\(^{\text{th}}\) term is \(13\).
Definition Arithmetic Sequence
An arithmetic sequence is a list of numbers where the same number is added or subtracted each time to get the next number.
The difference between two consecutive terms (two numbers that are next to each other in the sequence) is called the common difference.
The difference between two consecutive terms (two numbers that are next to each other in the sequence) is called the common difference.
Example
What is the 6\(^{\text{th}}\) term of this sequence?
| \(n\) | 1 | 2 | 3 | 4 | 5 | 6 |
| \(n^{\text{th}}\) term | 3 | 5 | 7 | 9 | 11 | ? |
The 6\(^{\text{th}}\) term is \(13\), because each term increases by \(2\).
Definition Geometric Sequence
A geometric sequence is a list of numbers where the same number is multiplied or divided each time to get the next number.
The ratio of two consecutive terms is called the common ratio.
The ratio of two consecutive terms is called the common ratio.
Example
What is the 5\(^{\text{th}}\) term of this sequence?
| \(n\) | 1 | 2 | 3 | 4 | 5 |
| \(n^{\text{th}}\) term | 2 | 4 | 8 | 16 | ? |
The 5\(^{\text{th}}\) term is \(32\), because each term is multiplied by \(2\).