1. PreCalculus 8-R Unit 8 Sequences, Series and Probability Review Problems

2. Find the third term of the sequence. a n = 2n + 9 a 3 = 15 1

3. Review Problems Find the second term of the sequence. 2

4. Review Problems Find the 200th term of the sequence. a n = 10 a 200 = 10 3

5. Review Problems Find the third term of the recursively defined sequence. a n = 5(a n – 1 – 5) and a 1 = 7 a 3 = 25 4

6. Review Problems Find the fifth term of the recursively defined sequence. a n = a n – 1 + a n – 2, a 1 = 1, a 2 = 2. a 5 = 8 5

7. Review Problems Find the nth term of the sequence. 2, 4, 8, 16,... a n = 2 n 6

8. Review Problems Find the partial sum S 5 of the sequence. 1, –1, 1, –1,... S 5 = 1 7

9. Review Problems Find the partial sum S n of the sequence. 8

10. Review Problems Find the first five terms and determine if the sequence is arithmetic. The sequence is arithmetic 9

11. Review Problems Find the 18th term of the arithmetic sequence. –t, – t + 3, – t + 6, – t + 9... 51 – t 10

12. Review Problems The 10th term of an arithmetic sequence is and the second term is. Find the first term. 11

13. Review Problems The 70th term of an arithmetic sequence is 107, and the common difference is 3. Find the first three terms. –100, –97, –94 12

14. Review Problems The 20th term of an arithmetic sequence is 97, and the common difference is 5. Find a formula for the nth term. 2 + 5(n – 1) 13

15. Review Problems Which term of the arithmetic sequence 3, 8, 13,... is 73? 15 14

16. Review Problems Find the partial sum S n of the arithmetic sequence that satisfies the following conditions. a = 3, d = 5, n = 20 1010 15

17. Review Problems A partial sum of an arithmetic sequence is given. Find the sum. 3 + 7 + 11 +... + 39 210 16

18. Review Problems A partial sum of an arithmetic sequence is given. Find the sum. 40.5 17

19. Review Problems Telephone poles are stored in a pile with 30 poles in the first layer, 29 in the second, and so on. If there are 12 layers, how many telephone poles does the pile contain? 294 poles 18

20. Review Problems Find the first five terms of the sequence and determine if it is geometric. If it is geometric express the nth term of the sequence in the standard form –3, 9, –27, 81, –243; 19

21. Review Problems Determine the 8th term of the geometric sequence. 20

22. Review Problems The first term of a geometric sequence is 6, and the second term is 3. Find the fifth term. 21

23. Review Problems Find the partial sum S n of the geometric sequence that satisfies the given conditions. a = 3, r = 4, n = 6 S n = 4,095 22

24. Review Problems Find the partial sum S n of the geometric sequence that satisfies the given conditions. S n = 30 23

25. Review Problems Find the sum of the infinite geometric series. 24

26. Review Problems Find the sum of the infinite geometric series. 25

27. Review Problems Find the sum of the infinite geometric series. 26

28. Review Problems A certain ball rebounds to the height from which it is dropped. Use an infinite geometric series to approximate the total distance the ball travels, after being dropped from 3 m above the ground, until it comes to rest. 18 m 27

29. Review Problems Principle of Mathematical Induction to show that the given statement is true for all natural numbers n 28

30. Review Problems Principle of Mathematical Induction to show that the given statement is true for all natural numbers n 29

31. Review Problems Principle of Mathematical Induction to show that the given statement is true for all natural numbers n 30

32. Review Problems Principle of Mathematical Induction to show that the given statement is true for all natural numbers n 31

33. Review Problems Expand the binomial 32

34. Review Problems Find the seventh term of the expansion of. 33

35. Review Problems Expand the binomial 34

36. Review Problems A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, the second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50 rows. Find the number of people that can be accommodated in the sixteenth row. 136 people 35

37. Review Problems Find the sum of the first 28 terms of the arithmetic sequence 4, 6, 8, 10, 12... 868 36

38. Review Problems Find S n if. 484 37

39. Review Problems Find the seventh term of the geometric sequence if a 1 = 2 and r = 4. 8192 38

40. Review Problems Find the sum of the first 7 terms of the series. 364.33 39

41. Review Problems Find the sum of the series. 40

42. Review Problems Find each sum. – 32.1416 41

43. Review Problems Use the principle of mathematical induction to show that the given statement is true for all natural numbers. 42

44. Review Problems Use the principle of mathematical induction to show that the given statement is true for all natural numbers. 43

45. Review Problems 16 44

46. Review Problems 8 45

47. Review Problems 24 46

48. Review Problems 60 47

49. Review Problems 35 48

50. Review Problems 1024 49

51. Review Problems 0.2 0.26 50

52. Review Problems 4/9 51

53. Review Problems 0.058 52

54. Review Problems 381,024 1260 53

55. Answers 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. a 3 = 15 a 200 = 10 a 3 = 25 a 5 = 8 a n = 2 n S 5 = 1 51 – t The sequence is arithmetic –100, –97, –94 2 + 5(n – 1) 15 1010 210 40.5 294 poles –3, 9, –27, 81, –243;

56. Answers 21. 22. 23. 24. 25. 26. 27. 28. proof 29. proof 30. proof 31. proof 32. 33. 34. 35. 36. 37. 38. 39. 40. S n = 4,095 S n = 30 18 m 136 people 868 484 8192 364.33

57. Answers 41. 42. proof 43. proof 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. – 32.1416 16 8 24 60 35 1024 0.20.26 4/9 0.058 381,0241260