A number pattern, also called a sequence, is simply an ordered list of numbers. We can categorize these sequences into two types: finite and infinite, based on whether they have a defined end or continue without limit.
Finite Number Patterns
A finite number pattern, or a finite sequence, is one where the list of numbers has a specific and known final value. This means the sequence stops at some point.
Key Characteristics
- Defined End: The sequence has a last term.
- Countable: The number of terms can be counted and is a specific number.
- Examples:
- 1, 3, 5, 7, 9
- 2, 4, 6, 8, 10, 12, 14
- 10, 20, 30, 40, 50, 60
- As per the reference, 1, 3, 5, …, 19 is a finite sequence, where the end value is 19.
Infinite Number Patterns
An infinite number pattern, or an infinite sequence, is a sequence where the numbers continue without an end. The list of numbers goes on forever.
Key Characteristics
- No Defined End: There is no last term in the sequence.
- Uncountable: The number of terms cannot be counted because they continue infinitely.
- Ellipsis (...): Often uses an ellipsis (...) to indicate that the sequence continues indefinitely.
- Examples:
- 2, 4, 6, 8, 10, ...
- 1, 3, 5, 7, 9, 11, ...
- 1, 2, 3, 4, 5, 6, 7, 8, ...
- As per the reference, 2, 5, 8, … is an example of an infinite sequence, indicating that the terms go on forever.
Summary Table
| Feature | Finite Sequence | Infinite Sequence |
|---|---|---|
| End | Has a defined final value | Continues without end |
| Number of Terms | Countable | Uncountable |
| Representation | Specific last term is known | Often uses '...' to indicate indefinite continuation |
In essence, the difference between finite and infinite sequences lies in whether they have a definite ending. Finite sequences stop, while infinite sequences continue on forever.
