1. Bell Quiz

2. Objectives Determine whether or not a sequence is arithmetic. Write a recursive formula for an arithmetic sequence. Find the nth term of an arithmetic sequence

3. Sequence Sequences of numbers can be formed using a variety of patterns and operations. A sequence is a list of numbers that follow a rule – each number in the sequence is called a term of the sequence. Here are a few examples of sequences: 1, 3, 5, 7, … 7, 4, 1, –2, … 2, 6, 18, 54, … 1, 4, 9, 16, …

4. Arithmetic Sequence In the previous examples, the first two sequences are a special type of sequence called an arithmetic sequences. An arithmetic sequence is a sequence that has a constant difference between two consecutive terms called the common difference.

5. Arithmetic Sequence To find the common difference, choose any term and subtract the previous term. In the first sequence, the common difference is 2. In the second sequence, the common difference is –3

6. Example 1 Recognizing Arithmetic Sequences Determine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms. 7, 12, 17, 22, …

7. Example 2 Recognizing Arithmetic Sequences Determine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms. 3, 6, 12, 24, …

8. Lesson Practice Determine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms. 7, 6, 5, 4, …

9. Lesson Practice Determine if the sequence is an arithmetic sequence. If yes, find the common difference and the next two terms. 10, 12, 15, 19, …

10. Arithmetic Sequence

12. Arithmetic sequences can be represented using a formula

13. Example 3 Using a Recursive Formula

14. Lesson Practice

15. Arithmetic Sequence A rule for finding any term in an arithmetic sequence can be developed by looking at a different pattern in the sequence 7, 11, 15, 19, …

16. Arithmetic Sequence To find the n th term of an arithmetic sequence we can use the formula:

17. Example 4 Finding the n th Term in Arithmetic Sequences

18. Lesson Practice

19. Example 5 Finding the n th Term in Arithmetic Sequences Find the 10 th term of the sequences 3, 11, 19, 27, …

20. Lesson Practice Find the 10 th term of the sequences 1, 10, 19, 28, …

21. Example 6 Finding the n th Term in Arithmetic Sequences

22. Lesson Practice

23. Example 7 Application: Seating for a Reception The first table at a reception will seat 9 guest while each additional table will seat 6 more guests. a.Write a rule to model the situation. b.Use the rule to find how many guests can be seated with ten tables.

24. Lesson Practice Flowers are purchased to put on tables at a reception. The head table needs to have 12 flowers and the other tables need to have 6 flowers each a.Write a rule to model the situation. b.Use the rule to find the number of flowers needed for 15 tables.