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.
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2, 4, 6, 8, …
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10, 50, 250, 1250, …
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3, 7, 11, 15, 19, …
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Based on this pattern, a n = 2 n.
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Based on this pattern, a n = 2(5 n ).
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Based on this pattern,
