X-3 -1 (12-180 2. 13X- 13X-39, DIvisAly Vision: L:3 618 Chapter 9 Sequences, Series, and Probability Writing the Terms of a Recursive Sequence In Exercises 51-56, write the first five terms of the sequence defined recursively. 4. i! (-1) 74. T j! 73. 21 97. Cor in a A Finding a Sum In Exercises 75-78, use a grapling quar 51. a1 utility to find the sum. 28, ak+1 %3D = a, - 4 52. a, = 3, a+1 = 2(az - 1) give 4(-1)* 75. ) k! 4 (-1)* 76. 53. a, = 81, a +1 = 3a %3D k=0 k + 1 54. a, 25 = 14, a+1 =(-2)a 55. a, = 1, a, = 2, a = a -2 + ża -1 77. E 47 (a) 78. 2n %3D (b) 56. ao = -1, a1 = 1, ar = a; -2 + ak-1 Using Sigma Notation to Write a Sum In Exercises 79–88, use sigma notation (c) I Fibonacci Sequence In Exercises 57 and 58, use the Fibonacci sequence. (See Example 5.) write the sum. • 98. Ph 1 57. Write the first 12 terms of the Fibonacci sequence 79. 3(1) 3(2) 3(3) The per 3(9) whose nth term is a, and the first 10 terms of the sequence given by physica 5 5 80. 1 + 1 can be a 1 + 2 1 + 3 1 + 15 An+1 Pn 0. n = 7, 8 81. 2() + 3+2) + 3] + 82. [1 - (91 + [1 - (9 + + [2@) + 3 + [1 - (91 83. 3 9 + 27 - 81 + 243 – 729 58. Using the defigiton for b, in Exercise S7, stow that can be defined reeursively by where n year, wi 84. 1 - + - corr pc Comemn 128 2007. b, = 1 + 12 85. 22 32 42 72 bn-1 Nationa 24 120 40,320 Health S Writing the Terms of a Sequence Involving Factorials In Exercises 59-62, write the first five terms of the sequence. (Assume that n begins with 0.) 1 1 (a) Writ 86. 3 2 4 3 . 5 of th 10 • 12 87. + 88. + + + 15 32 + cons (b) Wha 720 64 32 part 60. an 59. ал (n + 1)! n! Finding a Partial Sum of a Series 6O Exercises 89-92, find the (a) third, (b) fourth and (c) fifth partial sums of the series. (-1)2n+1 (2n + 1)! Explorati (-1)"(n + 3)! 62. an 61. an n! True or F 8 whether th 89. Σ 6. 08 90. Σ26 Simplifying a Factorial Expression In Exercises 63-66, simplify the factorial expression. answer. i= 1 91. Σ4-) 4. 99. (i? 12! 4! 63. 6! 64. 4! • 8! 92. Σ5-4" 100. 2i (2n - 1)! 66. (n + 1)! 65. Finding the Sum of an Infinit Series In Exercises 93-96, find the sum d Arithmeti following de (2n + 1)! n! Finding a Sum In Exercises 67-74, find n measuren the infinite series. the sum. 93. 10 4 4 101. Find th 68. 10 3i2 00 67. 94. balanc 10 $604.1 70. (2i – 1) 1 \k 69. 95. of a gra - 3 j=3j² 4. Σ-) 102. Proof 72. [(i - 1)2 + (i + 1)*] 71. (k + 1)2(k – 3) 96. i= 1 10 Solis Images/Shuttersto