Sequences
Numerical Sequence
Definition Numerical Sequence
A numerical sequence is a list of numbers that follow 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 in which the same value is added or subtracted each time to get the next term.
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 in which the same value is multiplied or divided each time to get the next term.
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 \(2\).