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All Textbook Solutions for Precalculus: Mathematics for Calculus - 6th Edition
25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63RE64RE65RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83RE1T2T3TA geometric sequence begins 12,3,34,316,364,. (a) Find the common ratio r for this sequence. (b) Find a formula for the nth term an of the sequence. (c) Find the tenth term of the sequence.The first term of a geometric sequence is 25, and the fourth term is 15. (a) Find the common ratio r and the fifth term. (b) Find the partial sum of the first eight terms.The first term of an arithmetic sequence is 10, and the tenth term is 2. (a) Find the common difference and the 100th term of the sequence. (b) Find the partial sum of the first ten terms.7TWrite the expression without using sigma notation, and then find the sum. (a) n=15(1n2) (b) n=36(1)n2n29T11T12TA puppy weighs 0.85 lb at birth, and each week he gains 24% in weight. Let an be his weight in pounds at the end of his nth week of life. (a) Find a formula for an. (b) How much does the puppy weigh when he is 6 weeks old? (c) Is the sequence a1, a2, a3, arithmetic, geometric, or neither?1PFitness Program Sheila decides to embark on a swimming program as the best way to maintain cardiovascular health. She begins by swimming 5 min on the first day, then adds 112 min every day after that. (a) Find a recursive formula for the number of minutes Tn that she swims on the nth day of her program. (b) Find the first 6 terms of the sequence Tn. (c) Find a formula for Tn. What kind of sequence is this? (d) On what day does Sheila attain her goal of swimming at least 65 min a day? (e) What is the total amount of time she will have swum alter 30 days?Monthly Savings Program Alice opens a savings account that pays 3% interest per year, compounded monthly. She begins by depositing 100 at the start of the first month and adds 100 at the end of each month, when the interest is credited. (a) Find a recursive formula for the amount An in her account at the end of the nth month. (Include the interest credited for that month and her monthly deposit.) (b) Find the first five terms of the sequence An. (c) Use the pattern you observed in (b) to find a formula for An. [Hint: To find the pattern most easily, its best not to simplify the terms too much] (d) How much has she saved after 5 years?4P5P6P7P8P9PA sequence is a function whose domain is __________.2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70ESigma Notation Write the sum using sigma notation. 71. 112+123+134++1999100072E73E74Enth Term of a Sequence Find a formula for the nth term of the sequence 2,22,222,2222, [Hint: Write each term as a power of 2.]76ECompound Interest Julio deposits 2000 in a savings account that pays 2.4% interest per year compounded monthly. The amount in the account after n months is given by An=2000(1+0.02412)n (a) Find the first six terms of the sequence. (b) Find the amount in the account after 3 years.78EPopulation of a City A city was incorporated in 2004 with a population of 35,000. It is expected that the population will increase at a rate of 2% per year. The population n years after 2004 is given by Pn=35,000(1.02)n (a) Find the first five terms of the sequence. (b) Find the population in 2014.80E81E82EAn arithmetic sequence is a sequence in which the __________ between successive terms is constant.2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60EDepreciation The purchase value of an office computer is 12,500. Its annual depreciation is 1875. Find the value of the computer after 6 years.Poles in a Pile Telephone poles are being stored in a pile with 25 poles in the first layer, 24 in the second, and so on. If there are 12 layers, how many telephone poles does the pile contain?Salary Increases A man gets a job with a salary of 30,000 a year. He is promised a 2300 raise each subsequent year. Find his total earnings for a 10-year period.Drive-In Theater A drive-in theater has spaces for 20 cars in the first parking row, 22 in the second, 24 in the third, and so on. If there are 21 rows in the theater, find the number of cars that can be parked.Theater Seating An architect designs a theater with 15 seats in the first row, 18 in the second, 21 in the third, and so on. If the theater is to have a seating capacity of 870, how many rows must the architect use in his design?66EThe Twelve Days of Christmas In the well-known song The Twelve Days of Christmas, a person gives his sweet-heart k gifts on the kth day for each of the 12 days of Christmas. The person also repeats each gift identically on each subsequent day. Thus on the 12th day the sweetheart receives a gift for the first day, 2 gifts for the second, 3 gifts for the third, and so on. Show that the number of gifts received on the 12th day is a partial sum of an arithmetic sequence. Find this sum.68EA geometric sequence is a sequence in which the __________ of successive terms is constant.2ETrue or False? If we know the first and second terms of a geometric sequence, then we can find any other term.4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E41E42E43E44E45E46E47E48E49E50E51E52E53E54E55E56E57E58E59E60E61E62E63E64E65E66E67E68E69E70E