292 CHAPTER 5 Number Theory and the Real Number System 5.6 In Exercises 65–72, evaluate each expression. 65. ⋅ 3 3 2 3 243 66. 8 8 5 3 64 67. 90 1 68. −5 3 1 125 69. ( ) 23 4 4096 70. −80 −1 71. − −7 2 − 1 49 72. ⋅ − 3 2 3 3 8 In Exercises 73–74, write each number in scientific notation. 73. 462,000 × 4.62 105 74. 0.0000158 × − 1.58 10 5 In Exercises 75–76, express each number in decimal notation. 75. × 2.8 105 280,000 76. 1.39 10 4 × − 0.000139 In Exercises 77–78, (a) perform the indicated operation and write your answer in scientific notation. (b) Confirm the result determined in part (a) by performing the calculation on a scientific calculator. 77. ( )( ) × × − 4 10 2 10 8 10 × − 8 10 2 78. × × − − 1.5 10 5 10 3 4 × 3.0 100 In Exercises 79–81, (a) perform the indicated calculation by first converting each number to scientific notation. Write your answer in decimal notation. (b) Confirm the result determined in part (a) by performing the calculation on a scientific calculator. 79. (550,000)(2,000,000) 1,100,000,000,000 80. 11,200,000,000 140,000,000 80 81. 0.000002 0.0000004 5 82. Space Distances The distance from Earth to the sun is about × 1.49 10 meters. 11 The distance from Earth to the moon is about × 3.84 10 meters. 8 The distance from Earth to the sun is about how many times larger than the distance from Earth to the moon? Use a scientific calculator and round your answer to the nearest whole number. 388 times 83. Outstanding Debt As a result of a recent water and sewer system improvement, the city of Galena, Illinois, has an outstanding debt of $20,000,000. If the population of Galena is 3600 people, how much would each person have to contribute to pay off the outstanding debt? ≈ $5555.56 5.7 In Exercises 84–85, determine whether the sequence is arithmetic or geometric. Then determine the next two terms of the sequence. 84. … 3, 9, 15, 21, Arithmetic; 27, 33 85. … , 1, 2, 4, 1 2 Geometric; 8, 16 In Exercises 86–89, determine the indicated term of the sequence with the given first term, a ,1 and common difference, d, or common ratio, r. 86. Determine a9 when = − = a d 6, 2. 1 10 87. Determine a10 when = − = a d 20, 5. 1 25 88. Determine a5 when = = a r 3, 2. 1 48 89. Determine a10 when = − = a r 1, 3. 1 −19,683 In Exercises 90 and 91, determine the sum of the arithmetic sequence. The number of terms, n, is given. 90. … = n 3, 6, 9, 12, , 150; 50 3825 91. … = n 0.5, 0.75, 1.00, 1.25, , 5.25; 20 57.5 In Exercises 92 and 93, determine the sum of the first n terms of the geometric sequence for the values of a1 and r. 92. = = = n a r 4, 3, 2 1 45 93. = = = − n a r 6, 1, 2 1 −21 In Exercises 94 and 95, first determine whether the sequence is arithmetic or geometric; then write an expression for the general or nth term, a .n 94. … 1, 4, 7, 10, Arithmetic; = − a n3 2 n 95. 2, 2, 2, 2, − − … Geometric; = − − a 2( 1) n n 1 5.8 96. Write down the first 15 terms of the Fibonacci sequence. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 In Exercises 97 and 98, determine whether the sequence is a Fibonacci-type sequence. If so, determine the next two terms. 97. … 0, 1, 1, 2, 2, 3, 3, 4, 4, No 98. 1, 0, 1, 1, 2, 3, 5, − − − − − − … Yes; 8, 13 − −
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