Introduction
Sequence and Series are the two most confusing words in the mathematics world. Most of the time, Sequence and Series are considered identical. But, they are not the same. This article will briefly discuss Sequence and Series and discuss the critical differences between Sequence and Series.
Sequence
It is a collection of numbers arranged in a specific order. The terms in a sequence can be repeated multiple times, but they need to follow some order or pattern.
Some examples of Sequence are given below:
-
1, 2, 3, 4, 5, 6
Here every term is one greater than the previous term. So, it follows a pattern. -
0, 5, 10, 15, 20
Here every term is five greater than the previous term. -
1, 10, 100, 1000
Here every term is ten times the previous term.
Sequences can be of two types:
- Finite Sequence: The number of terms is fixed and a limited number. All the examples discussed above were of a finite sequence.
- Infinite Sequence: The number of terms is infinite. Example: 1, 2, 3, 4, . . .
The Sequence can be represented as
where an is a term of the Sequence ranging from 1 to infinity.
Some types of Sequence are:
- Arithmetic Sequence
- Geometric Sequence
- Harmonic Sequence