A sequence.
A sequence is precisely a list of numbers, or more generally, elements, arranged in a specific order from the first term to the last term. This order is crucial; changing the order changes the sequence. Each individual number or element within the sequence is referred to as a term.
Here's a breakdown:
- Sequence: The overall list.
- Term: Each individual element in the list.
- Order: The defined arrangement from first to last.
Sequences can be finite (having a specific number of terms, like {1, 2, 3, 4}) or infinite (continuing indefinitely, like {1, 2, 3, ...}). The order is what distinguishes a sequence from a set, where the order of elements does not matter.
Examples:
- The sequence of even numbers: 2, 4, 6, 8, 10, ...
- The sequence of prime numbers: 2, 3, 5, 7, 11, ...
- A finite sequence: 1, 4, 9, 16, 25
In essence, a sequence represents an ordered arrangement of numbers or elements, making order a fundamental characteristic.
