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Name_________________________________ Date_______________ Arithmetic and Geometric Sequences Cheat SheetARITHMETIC SEQUENCEGEOMETRIC SEQUENCEDEFINITIONadd to get next term(common difference)multiply to get next term(common ratio)KEY WORDS“arithmetic”, “common difference”“geometric”, “common ratio”FORMULA (rule)un=u1+n-1dun=u1?rn-1FINDING THE PATTERNd=u2-u1ord=y2-y1x2-x1r=u2u1WORD PROBLEMS“increasing by a constant”“decreasing by a constant”“increasing by a percent”“decreasing by a percent”“doubles”, “triples”, “halves”, etc..Before you begin to answer the questions, be sure to identify if the sequence is arithmetic or geometric.Look for keywords in the question that can inform you if it is arithmetic or geometric.Write out the sequence and determine if you are adding or multiplying to get to your next term.Identify what the variable n represents in the context of the question. (nth row, nth day, nth year, etc…)Carefully read the question to see if they are asking you to find n or un. Use the context of the question!Name_________________________________ Date_______________ 6-7 Sequences Word ProblemsSequences Word Problems4852988224472Is this an arithmetic or geometric sequence? Why?0Is this an arithmetic or geometric sequence? Why?A theater has 35 seats in the first row. Each row has four more seats than the row before it. (a) Write an equation that represents the number of seats in the nth row.(b) Calculate the number of seats in the tenth row.(c) Calculate which row of the theater has 131 seats.4919027278130Is this an arithmetic or geometric sequence? Why?0Is this an arithmetic or geometric sequence? Why?On Monday Paco goes to a running track to train. He runs the first lap of the track?in 120 seconds. Each lap he runs takes 1.06 times as long as his previous lap.(a) Write a formula to find Paco’s running time on the nth lap.(b) Calculate the number of seconds it will take to Paco to run the fourth lap.The number of apartments in a housing development has been increasing by a constant amount every year.At the end of the first year the number of apartments was 150, and at the end of the sixth year the number of apartments was 600.(a) Calculate the number of apartments that the housing development increases by each year.490537563501Is this an arithmetic or geometric sequence? Why?0Is this an arithmetic or geometric sequence? Why?(b) ? ?Calculate the number of apartments in the housing development at the end of the tenth year.(c) Calculate the number of years it will take for there to be 2040 apartments in the housing development. A National Lottery is offering a prize in a new competition. The winner receives the following:$10 in the first week, $20 in the second week, $40 in the third week continuing to double for a total of 10 weeksBased on the information, write an equation to represent the amount of money you will receive after n weeks495744574295Is this an arithmetic or geometric sequence? Why?0Is this an arithmetic or geometric sequence? Why?(b) Calculate the amount you receive in the tenth week.Geometric Sequence Word Problems with PercentagesIf a question refers to a percent, this means you are dealing with a geometric sequence. When given a percent, the common ratio is the percent remaining of the previous term.DECREASE (LOSS)common ratio: r=1-%Ex 1: The current depression has caused a company to lose 12% of its current revenue each month during the year 2012. The company started out with $52,000 in the first month. What is the common ratio of this sequence?Ex 2: A certain water filtration system can remove 70% of the contaminants each time a sample of water is passed through it.What is the common ratio of this sequence?INCREASE (GAIN)common ratio: r=1+%Ex 1: Ben is playing a game similar to Monopoly. Each time Ben passes GO he receives 8% of the amount he already has. Ben starts with $100.What is the common ratio of this sequence?Ex 2: John’s starting salary at his new job is $50,000. His salary earns an increase of 4% each successive year.What is the common ratio of this sequence?4943158421958Is this an arithmetic or geometric sequence? Why?0Is this an arithmetic or geometric sequence? Why?On Vera’s 18th birthday she was given an allowance from her parents. She was given $80 the first month and an increase of 5% every month.(a) Calculate the common ratio of this sequence. (b) Calculate the value of Vera’s allowance after one year.Javier bought a car with an original price of $30,000 that depreciates by 30% each year. 4923790120650Is this an arithmetic or geometric sequence? Why?0Is this an arithmetic or geometric sequence? Why?(a) Calculate the common ratio of this sequence. (b) Calculate the value of Javier’s car after six years.PUTTING IT ALL TOGETHER7. Clara wants to buy some land. She can choose between two different payment options.Both options require her to pay for the land in 20 monthly installments.Option 1:The first installment is $2500. Each installment is $200 more than the one before.Option 2:The first installment is $2000. Each installment is 8? more than the one before.(a) Based on the information, write an equation to represent the amount of money Clara will pay after n months for: (i) option one; (ii) option two.Name_____________________________Date _____________________________Lesson 6-7: Homework1. Prachi is on vacation in the United States. She is visiting the Grand Canyon.When she reaches the top, she drops a coin down a cliff. The coin falls down a distance of?5?metres during the first second,?15?metres during the next second,?25?metres during the?third second and continues in this way. The distances that the coin falls during each second?forms an arithmetic sequence.(a) Write down the common difference,?d, of this arithmetic sequence.(b) ? ?Write down the distance the coin falls during the fourth second.2. The population of big cats in Africa is increasing at a rate of 5 % per year. At the beginning of 2004 the population was?10000.(a) Write down the population of big cats at the beginning of 2005.(b) Find the population of big cats at the beginning of 2010.3. A concert choir is arranged, per row, according to an arithmetic sequence. There are 20 singers in the fourth row and 32 singers in the eighth row.(a) Find the common difference of this arithmetic sequence. Find the number of singers in the first row.4. A certain school had a fun raising activity. Each board member was requested to sell one ticket on the first day and double the sales each day.(a) State the common ration of the sequence.(b) Calculate the number of tickets sold on the eighth day.(c) Calculate the day in which 512 tickets are sold. ................
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