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Concepts and Vocabulary

1. positive integers
3. 1
5. False
7. True
9. $a_{1} = 1, a_{2} = 4, a_{3} = 7, a_{4} = 10$ $a_{1} = 1, a_{2} = 4, a_{3} = 7, a_{4} = 10$
11. $a_{1} = 0, a_{2} = \frac{1}{2}, a_{3} = \frac{2}{3}, a_{4} = \frac{3}{4}$ $a_{1} = 0, a_{2} = \frac{1}{2}, a_{3} = \frac{2}{3}, a_{4} = \frac{3}{4}$
13. $a_{1} = - 1, a_{2} = - 4, a_{3} = - 9, a_{4} = - 16$ $a_{1} = - 1, a_{2} = - 4, a_{3} = - 9, a_{4} = - 16$
15. $a_{1} = 1, a_{2} = \frac{4}{3}, a_{3} = \frac{3}{2}, a_{4} = \frac{8}{5}$ $a_{1} = 1, a_{2} = \frac{4}{3}, a_{3} = \frac{3}{2}, a_{4} = \frac{8}{5}$
17. $a_{1} = 1, a_{2} = - 1, a_{3} = 1, a_{4} = - 1$ $a_{1} = 1, a_{2} = - 1, a_{3} = 1, a_{4} = - 1$
19. $a_{1} = \frac{5}{2}, a_{2} = \frac{11}{4}, a_{3} = \frac{23}{8}, a_{4} = \frac{47}{16}$ $a_{1} = \frac{5}{2}, a_{2} = \frac{11}{4}, a_{3} = \frac{23}{8}, a_{4} = \frac{47}{16}$
21. $a_{1} = 0.6, a_{2} = 0.6, a_{3} = 0.6, a_{4} = 0.6$ $a_{1} = 0.6, a_{2} = 0.6, a_{3} = 0.6, a_{4} = 0.6$
23. $a_{1} = - 1, a_{2} = \frac{1}{2}, a_{3} = - \frac{1}{6}, a_{4} = \frac{1}{24}$ $a_{1} = - 1, a_{2} = \frac{1}{2}, a_{3} = - \frac{1}{6}, a_{4} = \frac{1}{24}$
25. $a_{1} = - \frac{1}{3}, a_{2} = \frac{1}{9}, a_{3} = - \frac{1}{27}, a_{4} = \frac{1}{81}$ $a_{1} = - \frac{1}{3}, a_{2} = \frac{1}{9}, a_{3} = - \frac{1}{27}, a_{4} = \frac{1}{81}$
27. $a_{1} = \frac{e}{2}, a_{2} = \frac{e^{2}}{4}, a_{3} = \frac{e^{3}}{6}, a_{4} = \frac{e^{4}}{8}$ $a_{1} = \frac{e}{2}, a_{2} = \frac{e^{2}}{4}, a_{3} = \frac{e^{3}}{6}, a_{4} = \frac{e^{4}}{8}$
29.
31.
33.
35.
37.
39. $a_{n} = 3 n - 2$ $a_{n} = 3 n - 2$
41. $a_{n} = \frac{1}{n + 1}$ $a_{n} = \frac{1}{n + 1}$
43. $a_{n} = {(- 1)}^{n - 1} (2)$ $a_{n} = {(- 1)}^{n - 1} (2)$
45. $a_{n} = \frac{3^{n - 1}}{2^{n}}$ $a_{n} = \frac{3^{n - 1}}{2^{n}}$
47. $a_{n} = n (n + 1)$ $a_{n} = n (n + 1)$
49. $a_{n} = 2 - \frac{{(- 1)}^{n}}{n + 1}$ $a_{n} = 2 - \frac{{(- 1)}^{n}}{n + 1}$
51. $a_{n} = \frac{3^{n + 1}}{n + 1}$ $a_{n} = \frac{3^{n + 1}}{n + 1}$
53. $a_{1} = 2, a_{2} = 5, a_{3} = 8, a_{4} = 11, a_{5} = 14$ $a_{1} = 2, a_{2} = 5, a_{3} = 8, a_{4} = 11, a_{5} = 14$
55. $a_{1} = 3, a_{2} = 6, a_{3} = 12, a_{4} = 24, a_{5} = 48$ $a_{1} = 3, a_{2} = 6, a_{3} = 12, a_{4} = 24, a_{5} = 48$
57. $a_{1} = 7, a_{2} = - 11, a_{3} = 25, a_{4} = - 47, a_{5} = 97$ $a_{1} = 7, a_{2} = - 11, a_{3} = 25, a_{4} = - 47, a_{5} = 97$
59. $a_{1} = 2, a_{2} = \frac{1}{2}, a_{3} = 2, a_{4} = \frac{1}{2}, a_{5} = 2$ $a_{1} = 2, a_{2} = \frac{1}{2}, a_{3} = 2, a_{4} = \frac{1}{2}, a_{5} = 2$
61. $a_{1} = 25, a_{2} = - \frac{1}{125}, a_{3} = - 25, a_{4} = \frac{1}{125}, a_{5} = 25$ $a_{1} = 25, a_{2} = - \frac{1}{125}, a_{3} = - 25, a_{4} = \frac{1}{125}, a_{5} = 25$
63.
1. 2, 11, 26, 47, 74, 107, 146, 191, 242, 299
65.
1. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
67.
1. $0.5, - 1, 2, 0.5, - 1, 2, 0.5, - 1, 2, 0.5$ $0.5, - 1, 2, 0.5, - 1, 2, 0.5, - 1, 2, 0.5$
69. $\frac{1}{20}$ $\frac{1}{20}$
71. 12
73. $\frac{1}{n + 1}$ $\frac{1}{n + 1}$
75. $2 n + 1$ $2 n + 1$
77. 35
79. 55
81. 25
83. $\frac{853}{140}$ $\frac{853}{140}$
85. 183
87. $- 118$ $- 118$
89. $\sum_{k = 1}^{51} (2 k - 1)$ $\sum_{k = 1}^{51} (2 k - 1)$
91. $\sum_{k = 1}^{11} \frac{1}{5 k}$ $\sum_{k = 1}^{11} \frac{1}{5 k}$
93. $\sum_{k = 1}^{50} \frac{{(- 1)}^{k + 1}}{k}$ $\sum_{k = 1}^{50} \frac{{(- 1)}^{k + 1}}{k}$
95. $\sum_{k = 1}^{10} \frac{k}{k + 1}$ $\sum_{k = 1}^{10} \frac{k}{k + 1}$
97. 4620
99. $- 1.345$ $- 1.345$ (rounded to three decimal places)
101. 50

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Table of Contents for Concepts and Vocabulary

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Table of Contents for
Concepts and Vocabulary