Sequence
A sequence is a list of numbers in a certain order. Each number in a sequence is called a term. Each term in a sequence has a position (first, second, third and so on).
For example, consider the sequence 5, 15, 25, 35, …
In the sequence, each number is called a term. The number 5 has first position, 15 has second position, 25 has third position and so on.
You can also write an algebraic expression to represent the relationship between any term in a sequence and its position in the sequence.
In the above sequence, the difference between each term is 10 and let n represents the position in the sequence.
So, each term in the above sequence can be described as 10 n – 5.
A sequence is finite if it has a limited number of terms and infinite if it does not.
Finite sequence: {4, 8, 12, 16, … , 64}
The first of the sequence is 4 and the last term is 64. Since the sequence has a last term, it is a finite sequence.
Infinite sequence: {4, 8, 12, 16, 20, 24, …}
The first term of the sequence is 4 and it does not have the last term. Since the sequence has no last term, it is an infinite sequence.
Arithmetic and Geometric Sequences
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same.
Example: 10, 20, 30, 40, 50, …
Here, the common difference between any two consecutive terms is 10.
A geometric sequence is a sequence in which the common ratio between any two consecutive terms is the same.
Example: 2, 8, 32, 128, 512, …
Here, the common ratio between any two consecutive terms is 4.
