1. Slide 9 - 1 Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. All rights reserved. Chapter 9 Sequences; Induction; the Binomial Theorem

2. Slide 9 - 2 Copyright © 2009 Pearson Education, Inc. Evaluate a. b. c. d.

3. Slide 9 - 3 Copyright © 2009 Pearson Education, Inc. Evaluate a. b. c. d.

4. Slide 9 - 4 Copyright © 2009 Pearson Education, Inc. Write out the first five terms of a. b. c. d.

5. Slide 9 - 5 Copyright © 2009 Pearson Education, Inc. Write out the first five terms of a. b. c. d.

6. Slide 9 - 6 Copyright © 2009 Pearson Education, Inc. Write down the nth term of the sequence {a n } suggested by the pattern. a. c. b. d.

7. Slide 9 - 7 Copyright © 2009 Pearson Education, Inc. Write down the nth term of the sequence {a n } suggested by the pattern. a. c. b. d.

8. Slide 9 - 8 Copyright © 2009 Pearson Education, Inc. Write out the first four terms of the sequence defined recursively by a. b. c. d.

9. Slide 9 - 9 Copyright © 2009 Pearson Education, Inc. Write out the first four terms of the sequence defined recursively by a. b. c. d.

10. Slide 9 - 10 Copyright © 2009 Pearson Education, Inc. Write out the sum a. b. c. d.

11. Slide 9 - 11 Copyright © 2009 Pearson Education, Inc. Write out the sum a. b. c. d.

12. Slide 9 - 12 Copyright © 2009 Pearson Education, Inc. Express the sum using summation notation a. c. b. d.

13. Slide 9 - 13 Copyright © 2009 Pearson Education, Inc. Express the sum using summation notation a. c. b. d.

14. Slide 9 - 14 Copyright © 2009 Pearson Education, Inc. Find the sum of the sequence a.–40 b.–70 c.–61 d.–12

15. Slide 9 - 15 Copyright © 2009 Pearson Education, Inc. Find the sum of the sequence a.–40 b.–70 c.–61 d.–12

16. Slide 9 - 16 Copyright © 2009 Pearson Education, Inc. After working for 25 years you would like to have $600,000 in an annuity for early retirement. If the annuity interest rate is 7.5%, compounded monthly, what will your monthly deposit need to be? a.$1373.90b.$2080.03 c.$839.58d.$683.95

17. Slide 9 - 17 Copyright © 2009 Pearson Education, Inc. After working for 25 years you would like to have $600,000 in an annuity for early retirement. If the annuity interest rate is 7.5%, compounded monthly, what will your monthly deposit need to be? a.$1373.90b.$2080.03 c.$839.58d.$683.95

18. Slide 9 - 18 Copyright © 2009 Pearson Education, Inc. Given the arithmetic sequence Find the common difference and write out the first four terms. a. b. c. d.

19. Slide 9 - 19 Copyright © 2009 Pearson Education, Inc. Given the arithmetic sequence Find the common difference and write out the first four terms. a. b. c. d.

20. Slide 9 - 20 Copyright © 2009 Pearson Education, Inc. Find the nth term and a 21 of the arithmetic sequence {a n } whose initial term a 1 = 0 and a. b. c. d. common difference d =

21. Slide 9 - 21 Copyright © 2009 Pearson Education, Inc. Find the nth term and a 21 of the arithmetic sequence {a n } whose initial term a 1 = 0 and a. b. c. d. common difference d =

22. Slide 9 - 22 Copyright © 2009 Pearson Education, Inc. Find the fifteenth term of the arithmetic sequence a. b. c. d.

23. Slide 9 - 23 Copyright © 2009 Pearson Education, Inc. Find the fifteenth term of the arithmetic sequence a. b. c. d.

24. Slide 9 - 24 Copyright © 2009 Pearson Education, Inc. Find the first term, the common difference, and give a recursive formula for the arithmetic sequence whose 7th term is 31 and 16th term is –41. a. b. c. d.

25. Slide 9 - 25 Copyright © 2009 Pearson Education, Inc. Find the first term, the common difference, and give a recursive formula for the arithmetic sequence whose 7th term is 31 and 16th term is –41. a. b. c. d.

26. Slide 9 - 26 Copyright © 2009 Pearson Education, Inc. Find the sum of 7 + 14 + 21 + … + 672. a.31,920 b.32,256 c. d.32,592

27. Slide 9 - 27 Copyright © 2009 Pearson Education, Inc. Find the sum of 7 + 14 + 21 + … + 672. a.31,920 b.32,256 c. d.32,592

28. Slide 9 - 28 Copyright © 2009 Pearson Education, Inc. A theater has 20 rows with 24 seats in the first row, 28 in the second row, 32 in the third row, and so forth. How many seats are in the theater? a.2480 seats b.1280 seats c.1240 seats d.2560 seats

29. Slide 9 - 29 Copyright © 2009 Pearson Education, Inc. A theater has 20 rows with 24 seats in the first row, 28 in the second row, 32 in the third row, and so forth. How many seats are in the theater? a.2480 seats b.1280 seats c.1240 seats d.2560 seats

30. Slide 9 - 30 Copyright © 2009 Pearson Education, Inc. Find the common ratio and write out the first a. b. c. d. four terms of the geometric sequence

31. Slide 9 - 31 Copyright © 2009 Pearson Education, Inc. Find the common ratio and write out the first a. b. c. d. four terms of the geometric sequence

32. Slide 9 - 32 Copyright © 2009 Pearson Education, Inc. Determine whether the sequence a. c. b. d.Neither is arithmetic, geometric or neither. Find the common difference or common ratio.

33. Slide 9 - 33 Copyright © 2009 Pearson Education, Inc. Determine whether the sequence a. c. b. d.Neither is arithmetic, geometric or neither. Find the common difference or common ratio.

34. Slide 9 - 34 Copyright © 2009 Pearson Education, Inc. Determine whether the sequence a. c. b. d.Neither is arithmetic, geometric or neither. Find the common difference or common ratio.

35. Slide 9 - 35 Copyright © 2009 Pearson Education, Inc. Determine whether the sequence a. c. b. d.Neither is arithmetic, geometric or neither. Find the common difference or common ratio.

36. Slide 9 - 36 Copyright © 2009 Pearson Education, Inc. Find the fifth term and the nth term of the geometric sequence whose initial term is a = 6 and common ratio is r = –5. a. b. c. d.

37. Slide 9 - 37 Copyright © 2009 Pearson Education, Inc. Find the fifth term and the nth term of the geometric sequence whose initial term is a = 6 and common ratio is r = –5. a. b. c. d.

38. Slide 9 - 38 Copyright © 2009 Pearson Education, Inc. Find the nth term of the geometric sequence 5, –10, 20, –40, 80, …. a. b. c. d.

39. Slide 9 - 39 Copyright © 2009 Pearson Education, Inc. Find the nth term of the geometric sequence 5, –10, 20, –40, 80, …. a. b. c. d.

40. Slide 9 - 40 Copyright © 2009 Pearson Education, Inc. A new piece of equipment cost a company $48,000. Each year, for tax purposes, the company depreciates the value by 25%. What value should the company give the equipment after 7 years? a.$3 b.$6407 c.$8543 d.$12

41. Slide 9 - 41 Copyright © 2009 Pearson Education, Inc. A new piece of equipment cost a company $48,000. Each year, for tax purposes, the company depreciates the value by 25%. What value should the company give the equipment after 7 years? a.$3 b.$6407 c.$8543 d.$12

42. Slide 9 - 42 Copyright © 2009 Pearson Education, Inc. Find the sum a. c. b. d.

43. Slide 9 - 43 Copyright © 2009 Pearson Education, Inc. Find the sum a. c. b. d.

44. Slide 9 - 44 Copyright © 2009 Pearson Education, Inc. Determine whether the infinite geometric series a. c. b. d.Diverges converges, find its sum. converges or diverges. If it

45. Slide 9 - 45 Copyright © 2009 Pearson Education, Inc. Determine whether the infinite geometric series a. c. b. d.Diverges converges, find its sum. converges or diverges. If it

46. Slide 9 - 46 Copyright © 2009 Pearson Education, Inc. A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only 90% as far as on the previous swing. How far will it swing altogether before coming to a complete stop? a.89 inches b.800 inches c.400 inches d.178 inches

47. Slide 9 - 47 Copyright © 2009 Pearson Education, Inc. A pendulum bob swings through an arc 80 inches long on its first swing. Each swing thereafter, it swings only 90% as far as on the previous swing. How far will it swing altogether before coming to a complete stop? a.89 inches b.800 inches c.400 inches d.178 inches

48. Slide 9 - 48 Copyright © 2009 Pearson Education, Inc. Evaluate the expression a.1848 b.924 c.665,280 d.462

49. Slide 9 - 49 Copyright © 2009 Pearson Education, Inc. Evaluate the expression a.1848 b.924 c.665,280 d.462

50. Slide 9 - 50 Copyright © 2009 Pearson Education, Inc. Expand a. b. c. d. using the binomial theorem.

51. Slide 9 - 51 Copyright © 2009 Pearson Education, Inc. Expand a. b. c. d. using the binomial theorem.