You can tell a finite sequence from an infinite sequence by determining if the sequence ends or continues forever. According to the provided reference, a finite sequence ends, meaning it has a known final value. Conversely, an infinite sequence goes on forever, without a defined end.
Here's a breakdown:
Identifying Finite vs. Infinite Sequences
We can differentiate between finite and infinite sequences based on whether there is a last term:
- Finite Sequence: Has a last term. It is bounded and stops at a specific value.
- Infinite Sequence: Continues indefinitely. It does not have a last term and is not bounded in that sense.
Examples
Consider these examples, drawing from the reference:
- Finite Sequence Example: 1, 3, 5, ..., 19. This is a finite sequence because it has a last term, which is 19. We know where it ends.
- Infinite Sequence Example: 2, 5, 8, ... This is an infinite sequence because the ellipsis (...) indicates that the sequence continues indefinitely. We do not know where it ends; it doesn't end.
Key Differences Summarized
| Feature | Finite Sequence | Infinite Sequence |
|---|---|---|
| Last Term | Exists | Does not exist |
| Termination | Ends | Does not end; continues indefinitely |
| Representation | Can be fully written out (if short enough) | Represented with ellipsis (...) to show continuation |
In essence, if you can identify a final term, you're dealing with a finite sequence. If the sequence is presented with an ellipsis, suggesting it continues without end, it's an infinite sequence.
