What is the Difference Between Series and Sequence?

The main difference between a sequence and a series lies in how the elements are organized and their purpose. Here are the key differences:

• Sequence: A sequence is an arrangement of numbers or objects in a particular order, following a specific pattern or rules. The order of elements in a sequence is important, and each element has a specific position denoted by a number. Examples of sequences include arithmetic sequences, geometric sequences, harmonic sequences, and Fibonacci numbers.
• Series: A series is the sum of the elements of a sequence. The order of elements in a series is not important, and the focus is on the addition of the elements. A series can be finite or infinite, depending on whether the sequence is finite or infinite. Examples of series include geometric series and Fourier series.

In summary, a sequence is a list of elements arranged in a specific order, while a series is the sum of the elements in a sequence. The order of elements is crucial in a sequence, but it is not important in a series.

Comparative Table: Series vs Sequence

Here is a table highlighting the differences between a series and a sequence:

In summary, a sequence is an arrangement of numbers in a particular order or following a set of rules, while a series is the sum of the terms of a sequence. Sequences can be infinite or finite, and series can be arithmetic or geometric, depending on the sequence used to form them.