TOPIC: 9.2 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).
Vocabulary Key Concept Arithmetic Sequence Common Difference Arithmetic Mean Key Concept Arithmetic Sequence – recursive and explicit definitions
Is the sequence an arithmetic sequence?
Find the differences between consecutive terms. A. 3, 6, 9, 12, 15, … Find the differences between consecutive terms. 3 6 9 12 15 3 3 3 3 3 Each difference is __. The sequence is _____________ ________ . an arithmetic sequence
Find the differences between consecutive terms. 1 4 9 16 25 5 7 9 3 There is no common difference. The sequence is ______________________ . not an arithmetic sequence
2. What is the 100th term of the arithmetic sequence that begins 6, 11,… ?
Use the Explicit definition for the Arithmetic sequence. The first term is a = The common difference d = 6 11 - 6 = 5 Use the Explicit definition for the Arithmetic sequence. an = a + (n – 1)d a100 = 6 + (100 – 1)5 a100 = 501
3. What is the 46th term of the arithmetic sequence that begins 3, 5, 7,… ?
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
4. Use the Arithmetic Mean to calculate the missing term of the arithmetic sequence 15, __, 59,… .
Arithmetic Mean =
The arithmetic sequence 15, __, 59. 37
5. What are the second, third and fourth terms of the arithmetic sequence 20, _, _, _, 56,… ?
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
Use the Recursive definition for the Arithmetic sequence.
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,…
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?
Hmwk 9.2 A: Practice: 7 – 23 ODD Work on the Study Plan
H 9.2A Answers Practice: 7 – 23 ODDS ONLY
Notes 9.2 Calculator
6. Find the 17th term of the sequence.
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
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 = -57 + (17 – 1)5 a17 = -57 + (16)5 a17 = 23
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?
Hmwk 9.2 B Math XL Work on the Study Plan