Solutions

Solutions to Try Its

1. The sequence is arithmetic. The common difference is −2.

2. The sequence is not arithmetic because 3−1≠6−3.

3. {1,6,11,16,21}

4. a2=2

5. a1=25an=an−1+12, for n≥2

6. an=53−3n

7. There are 11 terms in the sequence.

8. The formula is Tn=10+4n, and it will take her 42 minutes.

Solutions to Odd-Numbered Exercises

1. A sequence where each successive term of the sequence increases (or decreases) by a constant value.

3. We find whether the difference between all consecutive terms is the same. This is the same as saying that the sequence has a common difference.

5. Both arithmetic sequences and linear functions have a constant rate of change. They are different because their domains are not the same; linear functions are defined for all real numbers, and arithmetic sequences are defined for natural numbers or a subset of the natural numbers.

7. The common difference is 12

9. The sequence is not arithmetic because 16−4≠64−16.

11. 0,23,43,2,83

13. 0,−5,−10,−15,−20

15. a4=19

17. a6=41

19. a1=2

21. a1=5

23. a1=6

25. a21=−13.5

27. −19,−20.4,−21.8,−23.2,−24.6

29. a1=17;an=an−1+9n≥2

31. a1=12;an=an−1+5n≥2

33. a1=8.9;an=an−1+1.4n≥2

35. a1=15;an=an−1+14n≥2

37. 1=16;an=an−1−1312n≥2

39. a1=4; an=an−1+7; a14=95

41. First five terms: 20,16,12,8,4.

43. an=1+2n

45. an=−105+100n

47. an=1.8n

49. an=13.1+2.7n

51. an=13n−13

53. There are 10 terms in the sequence.

55. There are 6 terms in the sequence.

57. The graph does not represent an arithmetic sequence.

59.
Graph of a scattered plot with labeled points: (1, 9), (2, -1), (3, -11), (4, -21), and (5, -31). The x-axis is labeled n and the y-axis is labeled a_n.

61. 1,4,7,10,13,16,19

63.
Graph of a scattered plot with labeled points: (1, 1), (2, 4), (3, 7), (4, 10), and (5, 13). The x-axis is labeled n and the y-axis is labeled a_n.

65.
Graph of a scattered plot with labeled points: (1, 5.5), (2, 6), (3, 6.5), (4, 7), and (5, 7.5). The x-axis is labeled n and the y-axis is labeled a_n.

67. Answers will vary. Examples: an=20.6n and an=2+20.4n.

69. a11=−17a+38b

71. The sequence begins to have negative values at the 13th term, a13=−13

73. Answers will vary. Check to see that the sequence is arithmetic. Example: Recursive formula: a1=3,an=an−1−3. First 4 terms: 3,0,−3,−6a31=−87