1071 11.3 Geometric Sequences and Series 78. Perimeter and Area of Triangles In Exercise 77, if the process could be continued indefinitely, what would be the total perimeter of all the triangles? What would be the total area of all the triangles, disregarding the overlapping? 79. Salaries A student is offered a 6-week summer job and is asked to select one of the following salary options. Option 1: $5000 for the first day with a $10,000 raise each day for the remaining 29 days (that is, $15,000 for day 2, $25,000 for day 3, and so on) Option 2: $0.01 for the first day with the pay doubled each day (that is, $0.02 for day 2, $0.04 for day 3, and so on) Which option has a greater total salary? 80. Number of Ancestors A genealogical Web site allows a person to identify all of her or his ancestors who lived during the last 300 yr. Assuming that each generation spans about 25 yr, guess the number of ancestors that would be found during the 12 generations. Then use the formula for a geometric series to find the correct value. Future Value of an Annuity Find the future value of each annuity. See Example 9. 81. There are payments of $1000 at the end of each year for 9 yr at 3% interest compounded annually. 82. There are payments of $800 at the end of each year for 12 yr at 2% interest compounded annually. 83. There are payments of $2430 at the end of each year for 10 yr at 1% interest compounded annually. 84. There are payments of $1500 at the end of each year for 6 yr at 0.5% interest compounded annually. 85. Refer to Exercise 83. Use the answer and recursion to find the balance after 11 yr. 86. Refer to Exercise 84. Use the answer and recursion to find the balance after 7 yr. 87. Individual Retirement Account Starting on his 40th birthday, Miguel deposits $2000 per year in an Individual Retirement Account until age 65 (last payment at age 64). Find the total amount in the account if he had a guaranteed interest rate of 2% compounded annually. 88. Retirement Savings To save for retirement, Mort put $3000 at the end of each year into an ordinary annuity for 20 yr at 1.5% annual interest. At the end of year 20, what was the amount of the annuity? 89. Show that the formula for future value of an annuity gives the correct answer when compared to the solution in Example 9. 90. The screen here shows how the TI-84 Plus calculator computes the future value of the annuity described in Example 9. Use a calculator with this capability to support the answers in Exercises 81–88. 91. Concept Check Suppose that a1, a2, a3, a4, a5, c is a geometric sequence. Is the sequence a1, a3, a5, c geometric? 92. Concept Check Is the sequence log6,log36,log1296,log1,679,616, c a geometric sequence?
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