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 nis used to denote the different terms in a sequence. 

The expression a nis 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. 

  1. 2, 4, 6, 8, …
  2. 10, 50, 250, 1250, …
  3. 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, 

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