1. TOPIC:
Arithmetic Sequences
Name: Daisy Basset Date :
Period: Subject:
Notes
Objective:
Construct linear functions, including arithmetic sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

2. Vocabulary Key Concept
Arithmetic Sequence
Common Difference
Arithmetic Mean
 Key Concept
Arithmetic Sequence – recursive and explicit definitions

3. Is the sequence an arithmetic sequence?

4. Find the differences between consecutive terms.
A. 3, 6, 9, 12, 15, …
Find the differences between consecutive terms. 3 3 3 3 3
Each difference is __. The sequence is _____________ ________ .
an arithmetic
sequence

5. Find the differences between consecutive terms. 5 7 9 3
There is no common difference. The sequence is ______________________ .
not an arithmetic sequence

6. 2. What is the 100th term of the arithmetic sequence that begins 6, 11,… ?

7. Use the Explicit definition for the Arithmetic sequence.
The first term is a = The common difference d = 6 = 5
Use the Explicit definition for the Arithmetic sequence.
an = a + (n – 1)d
a100 = 6 + (100 – 1)5
a100 = 501

8. 3. What is the 46th term of the arithmetic sequence that begins 3, 5, 7,… ?

9. Use the Explicit definition for the Arithmetic sequence.
The first term is a = The common difference d = 3
5 - 3 = 2
Use the Explicit definition for the Arithmetic sequence.
an = a + (n – 1)d
a46 = 3 + (46 – 1)2
a46 = 93

10. 4. Use the Arithmetic Mean to calculate the missing term of the arithmetic sequence 15, __, 59,… .

11. Arithmetic Mean =

12. The arithmetic sequence 15, __, 59.37

13. 5. What are the second, third and fourth terms of the arithmetic sequence 20, _, _, _, 56,… ?

14. Use the Explicit definition for the Arithmetic sequence.
The first term is a = The fifth term is a5 = 20 56
Use the Explicit definition for the Arithmetic sequence.
an = a + (n – 1)d
a5 = a + (n – 1)d
56 = 20 + (5 – 1)d

15. Use the Recursive definition for the Arithmetic sequence.

16. an = an-1 + d 20, 29, 38, 47, 56,… 20,_____, __, __, 56,… 20+9 29+9
20, 29, ____, _, 56,…
20, 29, 38, _____, 56,…
38+9
20, 29, 38, 47, 56,…

17. Summary
Summarize/reflect  D
 What did I do? L 
 What did I learn?  I
 What did I find most interesting? Q 
 What questions do I still have? What do I need clarified?

18. Hmwk 9.2 A:
Practice: 7 – 23 ODD
Work on the Study Plan

19. H 9.2A Answers
Practice: 7 – 23 ODDS ONLY

20. Notes 9.2
Calculator

21. 6. Find the 17th term of the sequence.

22. Use the Explicit definition for the Arithmetic sequence.
a16 = 18, d = 5
Use the Explicit definition for the Arithmetic sequence.
an = a + (n – 1)d
a16 = a + (16 – 1)5
18 = a + (15)5
18 = a + 75
-57 = a

23. Use the Explicit definition for the Arithmetic sequence.
a16 = 18, d = 5, a = -57
Use the Explicit definition for the Arithmetic sequence.
a = a + (n – 1)d
a17 = (17 – 1)5
a17 = (16)5
a17 = 23

24. Summary
Summarize/reflect  D
 What did I do? L 
 What did I learn?  I
 What did I find most interesting? Q 
 What questions do I still have? What do I need clarified?

25. Hmwk 9.2 B Math XL
Work on the Study Plan