1060 CHAPTER 11 Further Topics in Algebra 67. a 3 i=1 1i + 42 68. a 5 i=1 1i - 82 69. a10 j=1 12j + 32 70. a15 j=1 15j - 92 71. a12 i=4 1-5 - 8i2 72. a19 k=5 1-3 - 4k2 73. a1000 i=1 i 74. a1000 i=1 -i 75. a100 k=1 2k 76. a100 k=112k - 12 77. a50 j=10 5j 78. a80 j=20 3j Use the summation feature of a graphing calculator to evaluate the sum of the first ten terms of each arithmetic series with an defined as shown. In Exercises 81 and 82, round to the nearest thousandth. 79. an = 4.2n + 9.73 80. an = 8.42n + 36.18 81. an = 28 n + 23 82. an = -2 3 4 n + 27 Solve each problem. 83. Integer Sum Find the sum of all the integers from 51 to 71. 84. Integer Sum Find the sum of all the integers from -8 to 30. 85. Clock Chimes If a clock strikes the proper number of chimes each hour on the hour, how many times will it chime in a month of 30 days? 86. Telephone Pole Stack A stack of telephone poles has 30 in the bottom row, 29 in the next, and so on, with one pole in the top row. How many poles are in the stack? 87. Population Growth Five years ago, the population of a city was 49,000. Each year the zoning commission permits an increase of 580 in the population. What will the maximum population be 5 yr from now? 88. Slide Supports A super slide of uniform slope is to be built on a level piece of land. There are to be 20 equally spaced vertical supports, with the longest support 15 m long and the shortest 2 m long. Find the total length of all the supports. 89. Rungs of a Ladder How much material will be needed for the rungs of a ladder of 31 rungs, if the rungs taper uniformly from 28 in. to 18 in.? 90. (Modeling) Children’s Growth Pattern The normal growth pattern for children aged 3–11 follows that of an arithmetic sequence. An increase in height of about 6 cm per year is expected. Thus, 6 would be the common difference of the sequence. For example, a child who measures 96 cm at age 3 would have his expected height in subsequent years represented by the sequence 102, 108, 114, 120, 126, 132, 138, 144. Each term differs from the adjacent terms by the common difference, 6. (a) If a child measures 98.2 cm at age 3 and 109.8 cm at age 5, what would be the common difference of the arithmetic sequence describing his yearly height? (b) What would we expect his height to be at age 8? 91. Concept Check Suppose that a1, a2, a3, a4, a5, c is an arithmetic sequence. Is a1, a3, a5, c an arithmetic sequence? 92. Concept Check Is the sequence log 2, log 4, log 8, log 16, c an arithmetic sequence? Evaluate each sum. See Example 9.
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