In mathematics, a sequence is a list of numbers arranged in a specific order. Each number in the sequence is called a term, and the sequence can be either finite or infinite. For example, the numbers 1, 2, 3, 4, and 5 can be expressed as a finite sequence, while the sequence of all natural numbers is infinite.
On the other hand, a series is what you get when you add the terms of a sequence together. It represents the sum of the elements of a sequence. For instance, if you take the sequence of numbers 1, 2, 3, 4, and 5 and sum them up, you get the series 1 + 2 + 3 + 4 + 5, which equals 15.
In summary, the key difference lies in their definitions: a sequence refers to the ordered list of numbers, while a series refers to the sum of the numbers in that list. Understanding this distinction is essential for further studies in mathematics, particularly in topics like calculus and analysis.