1069 11.3 Geometric Sequences and Series Use the summation feature of a graphing calculator to evaluate each sum. Round to the nearest thousandth. 65. a10 i=1 11.42i 66. a 6 j=1 -13.62j 67. a 8 j=3 210.42j 68. a 9 i=4 310.252i Solve each problem. See Examples 1–8. 69. (Modeling) Investment for Retirement According to T. Rowe Price Associates, a person with a moderate investment strategy and n years to retirement should have accumulated savings of an percent of his or her annual salary. The geometric sequence an = 127610.9162n gives the appropriate percent for each year n. (a) Find a1 and r. Round a1 to the nearest whole number. (b) Find and interpret the terms a10 and a20. Round to the nearest whole number. 70. (Modeling) Investment for Retirement Refer to Exercise 69. For someone who has a conservative investment strategy with n years to retirement, the geometric sequence is an = 127810.9352n. (Data from T. Rowe Price Associates.) (a) Repeat part (a) of Exercise 69. (b) Repeat part (b) of Exercise 69. (c) Why are the answers in parts (a) and (b) greater than those in Exercise 69? 71. (Modeling) Bacterial Growth Suppose that a strain of bacteria will double in size and then divide every 40 minutes. Let a1 be the initial number of bacteria cells, a2 the number after 40 minutes, and an the number after 401n - 12 minutes. (a) Write a formula for the nth term an of the geometric sequence a1, a2, a3, c, an, c. (b) Determine the first value for n where an 71,000,000 if a1 = 100. (c) How long does it take for the number of bacteria to exceed one million? Evaluate each sum. See Example 8. 53. 18 + 6 + 2 + 2 3 + g 54. 100 + 10 + 1 + g 55. 1 4 - 1 6 + 1 9 - 2 27 + g 56. 4 3 + 2 3 + 1 3 + g 57. a ∞ i=1 3a 1 4b i-1 58. a ∞ i=1 5a1 4b i-1 59. a ∞ k=1 3-k 60. a ∞ k=1 10-k 61. a ∞ i=1 a2 3b a1 4b i-1 62. a ∞ i=1 a1 5b a2 5b i-1 63. a ∞ i=1 a 3 7b i 64. a ∞ i=1 a 5 9b i
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