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
In the sequence, each number is called a term. The number has first position, has second position, has third position and so on.
The term of a sequence is sometimes written .
Often, you can find an algebraic expression to represent the relationship between any term in a sequence and its position in the sequence.
In the above sequence, the term can be calculated using the equation .
Finite and Infinite Sequences
A sequence is finite if it has a limited number of terms and infinite if it does not.
The first of the sequence is and the last term is . Since the sequence has a last term, it is a finite sequence.
The first term of the sequence is . The "..." at the end indicates that the sequence goes on forever; it does not have a last term. It is an infinite sequence.
Increasing and Decreasing Sequences
An increasing sequence is one in which every term is greater than the previous term. That is, .
The following two sequences are both increasing.
A decreasing sequence is one in which every term is greater than the previous term. That is, .
The following two sequences are both decreasing.
It is possible for a sequence to be neither increasing nor decreasing:
Arithmetic and Geometric Sequences
An arithmetic sequence is a sequence in which the difference between any two consecutive terms is the same.
Here, the common difference between any two consecutive terms is .
Here, the common ratio between any two consecutive terms is .