The key difference between a sequence and an infinite sequence lies in the termination point: a sequence can be finite (ending after a certain number of terms), while an infinite sequence continues endlessly.
Here's a breakdown:
-
Sequence: A sequence is an ordered list of elements (usually numbers). It has a defined starting point and can be either finite or infinite.
- Finite Sequence: A finite sequence has a specific number of terms and ends at a certain point. For example, the sequence of even numbers less than 10:
2, 4, 6, 8. - Example: The sequence of the first 5 prime numbers:
2, 3, 5, 7, 11.
- Finite Sequence: A finite sequence has a specific number of terms and ends at a certain point. For example, the sequence of even numbers less than 10:
-
Infinite Sequence: An infinite sequence is a sequence that continues without end. It has a defined starting point but no termination point.
- Example: The sequence of all positive integers:
1, 2, 3, 4, 5, ...(the ellipsis "..." indicates that the sequence continues indefinitely). - Example: The sequence of even numbers:
2, 4, 6, 8, 10, ...
- Example: The sequence of all positive integers:
| Feature | Sequence | Infinite Sequence |
|---|---|---|
| Termination | Can be finite or infinite | Always infinite |
| Number of terms | Can be finite or infinite | Infinite |
| Ending Point | May have an ending point | No ending point |
In essence, an infinite sequence is just a specific type of sequence – one that never ends. All infinite sequences are sequences, but not all sequences are infinite.
