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