8.1 Sequences.

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Presentation transcript:

8.1 Sequences

Here are two examples of . Sequence 1: Sequence 2: 3, 6, 9, 12, 15 3, 6, 9, 12, 15,… The numbers in the sequences are called . Sequence 1 is called a sequence because it has a last term. Sequence 2 is called an sequence because it continues without stopping. sequences terms finite infinite

An sequence is any sequence in which the next term is obtained by adding a fixed number, called the , to the preceding term. arithmetic common difference

State whether each of the following is an arithmetic sequence State whether each of the following is an arithmetic sequence. If it is, give the next term. 4, 1, -2, -5,… 2. 1, 4, 9, 16,… 3.

There are two different ways to write the equation for a sequence There are two different ways to write the equation for a sequence. In either formula, the n represents the term number. We use subscript to denote a specific term. For example, is the first term of the arithmetic sequence and is the nth term of the arithmetic sequence.

Recursive Formula a1 Recursive formulas give , which is the term of the sequence and then give a rule or formula for subsequent terms using the term to find the next. Example: , For arithmetic sequences, we can write the recursive rule as where d is the common difference. first previous

State the second and third term of the arithmetic sequence whose first term is given. 4. 5. 6.

State the first four terms of the sequence State the first four terms of the sequence. If it is arithmetic, give the common difference. 7. 8.

Specify each sequence recursively. 9. 13, 7, 1, -5,… 10. 6, 12, 24, 48,…

Explicit formula A sequence can be specified by giving the value of any term as a function of its in the sequence, n. Example: We will learn rules for explicit formulas for specific types of sequences in future lessons. order

State the first four terms of the sequence State the first four terms of the sequence. If the sequence is arithmetic, give the common difference. 11. 12.

Specify each rule explicitly. 13. 2, 6, 10, 14,… 14. 1, 4, 9, 16,…