Definition and Examples of Sequences
A sequence is an ordered list of numbers .
The three dots mean to continue forward in the pattern established. Each number in the sequence is called a term. In the sequence 1, 3, 5, 7, 9, …, 1 is the first term, 3 is the second term, 5 is the third term, and so on. The notation a _{1}, a _{2}, a _{3},… a _{n} is used to denote the different terms in a sequence.
The expression a _{n} is referred to as the general or nth term of the sequence.
Example 1
Write the first five terms of a sequence described by the general term a _{n} = 3 n + 2.
Therefore, the first five terms are 5, 8, 11, 14, and 17.
Example 2
Write the first five terms of a _{n} = 2(3 ^{n – 1 }).
Therefore, the first five terms are 2, 6, 18, 54, and 162.
Example 3
Find an expression for the nth term of each sequence.

2, 4, 6, 8, …

10, 50, 250, 1250, …

3, 7, 11, 15, 19, …

Based on this pattern, a _{n} = 2 n.

Based on this pattern, a _{n} = 2(5 ^{n }).

Based on this pattern,