1. Copyright © 2007 Pearson Education, Inc. Slide 8-1

2. Copyright © 2007 Pearson Education, Inc. Slide 8-2 Chapter 8: Further Topics in Algebra 8.1Sequences and Series 8.2Arithmetic Sequences and Series 8.3Geometric Sequences and Series 8.4The Binomial Theorem 8.5Mathematical Induction 8.6Counting Theory 8.7Probability

3. Copyright © 2007 Pearson Education, Inc. Slide 8-3 5, 9, 13, 17 … is an example of an arithmetic sequence since 4 is added to each term to get the next term. The fixed number added is called the common difference. 8.2 Arithmetic Sequences and Series An arithmetic sequence is a sequence in which each term is obtained by adding a fixed number to the previous term.

4. Copyright © 2007 Pearson Education, Inc. Slide 8-4 8.2 Finding a Common Difference Example Find the common difference d for the arithmetic sequence –9, –7, –5, –3, –1, … Solution d can be found by choosing any two consecutive terms and subtracting the first from the second: d = –5 – (–7) = 2.

5. Copyright © 2007 Pearson Education, Inc. Slide 8-5 8.2 Arithmetic Sequences and Series nth Term of an Arithmetic Sequence In an arithmetic sequence with first term a 1 and common difference d, the nth term a n, is given by

6. Copyright © 2007 Pearson Education, Inc. Slide 8-6 8.2 Finding Terms of an Arithmetic Sequence Example Find a 13 and a n for the arithmetic sequence –3, 1, 5, 9, … Solution Here a 1 = –3 and d = 1 – (–3) = 4. Using n=13, In general

7. Copyright © 2007 Pearson Education, Inc. Slide 8-7 8.2 Find the nth term from a Graph Example Find a formula for the nth term of the sequence graphed below.

8. Copyright © 2007 Pearson Education, Inc. Slide 8-8 8.2 Find the nth term from a Graph Solution The equation of the dashed line shown Below is y = –.5x +4. The sequence is given by a n = –.5n +4 for n = 1, 2, 3, 4, 5, 6.

9. Copyright © 2007 Pearson Education, Inc. Slide 8-9 8.2 Arithmetic Sequences and Series Sum of the First n Terms of an Arithmetic Sequence If an arithmetic sequence has first term a 1 and common difference d, the sum of the first n terms is given by or

10. Copyright © 2007 Pearson Education, Inc. Slide 8-10 8.2 Using The Sum Formulas Example Find the sum of the first 60 positive integers. Solution The sequence is 1, 2, 3, …, 60 so a 1 = 1 and a 60 = 60. The desired sum is

11. Copyright © 2007 Pearson Education, Inc. Slide 8-11 8.2 Using Summation Notation Example Evaluate the sum. Solution The sum contains the terms of an arithmetic sequence having a 1 = 4(1) + 8 = 12 and a 10 = 4(10) + 8 = 48. Thus,