1. 2, 4, 6, 8, 10, … 2. 15, 11, 7, 3, -1, … 3. -12, -7, -2, 3, 8, …
17
1. 2, 4, 6, 8, 10, … 2. 15, 11, 7, 3, -1, … 3. -12, -7, -2, 3, 8, … Warm-Up: February 26, 2013 Write the next 3 numbers in the pattern
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Transcript of 1. 2, 4, 6, 8, 10, … 2. 15, 11, 7, 3, -1, … 3. -12, -7, -2, 3, 8, …
1. 2, 4, 6, 8, 10, …
2. 15, 11, 7, 3, -1, …
3. -12, -7, -2, 3, 8, …
Warm-Up: February 26, 2013Write the next 3 numbers in the pattern
Homework Questions?
Arithmetic SequencesSection 11.2
How can we recognize and utilize a pattern in a sequence of numbers.
Essential Question
An arithmetic sequence is a sequence whose successive terms differ by the same number, d, called the common difference.
Definition
t1 is the first term n is an integer tn is the nth term d is the common difference
The Equation: dnttn 11
n and m are integers tn is the nth term tm is the mth term d is the common difference
Better Equation: dmntt mn
Based on the terms given, state whether or not each sequence is arithmetic. If it is, identify the common difference, d.
0, -6, -12, -18, -24, …
Example 1: Page 703 #15
Based on the terms given, state whether or not each sequence is arithmetic. If it is, identify the common difference, d.
-3, 0, 3, 6, 9, …
You-Try #1: Page 703 #11
Based on the terms given, state whether or not each sequence is arithmetic. If it is, identify the common difference, d.
You-Try #2: Page 703 #23
,...9
8,8
7,7
6,6
5,5
2
1. Find the common difference2. Find the first term3. Find the nth term
OR4. Find the common difference5. Fill in the blanks by adding d until you get
to the nth term
Finding a specific term
Find the indicated term given two other terms.
10th term; t1 = 2.1 and t4 = 1.83
Example 3: Page 704 #53
Find the indicated term given two other terms.
5th term; t3 = 10 and t7 = 26
You-Try #3: Page 704 #51
Arithmetic means are the terms between two nonconsecutive terms of an arithmetic sequence.
1. Let the first number be t1 and the second number by tn
2. n is the number of arithmetic means + 23. Use the equation to solve for d4. Add d to find the missing terms
Arithmetic Means
Find the two arithmetic means between 5.26 and 6.34
Example 4: Page 704 #73
Find the three arithmetic means between 18 and -10
You-Try #4: Page 704 #71
Pages 703-704 #9-29 odd, 51-55 odd, 69-73 odd
Assignment
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