Welcome To Common Core Algebra I



Common Core Algebra Unit 12: Sequences 3/1/17Lesson 3: Geometric Sequences (Explicit)Objective: SWBAT identify a geometric sequence and apply the explicit formula to situations.Do Now: In the movie "Pay it Forward" the main character, a young boy, determines that he can make a significant difference in the world by creating a chain of events. During the movie he helps three people, who each help three people and so on.a) How many people’s lives would be affected in the 6th round of this pattern? 1, 3, 9, ______, ______, ______ b) Identify the pattern in this sequence of numbers.What is a Geometric Sequence?54857658826500To find the common ratio: Divide any term by the previous term. The common ratio in this example is ______. To find the next term: Multiply the previous term by the common ratio. The next term in this example is ______.Group Task:Let's take a look at some sequences...is there a common ratio? If so, find the next term in the sequence.Writing Geometric Sequences as FunctionsYou can use the first term and the common ratio to write a function rule that describes a geometric sequence. Assume the first term is 4 and the common ratio is 3.a1 = ______ r = ______160528014414500Model Example:Given the following geometric sequence: 1, 4, 16, 64, …a) Define the sequence explicitly. b) Find the 11th term. Check for Understanding:Given the following geometric sequence: 4, -20, 100…a) Define the sequence explicitly. b) Find the 6th term. Group Task:The number of bacteria in a culture doubles each hour. The table shows the number of new bacteria for each hour.22860009017000Write an equation that can be used to find the number of new bacteria after n hours. Find the number of bacteria after 5 hours.After how many hours is the number of bacteria 7680?Check for Understanding:A digital city map displays an area of 544 square units. After you zoom in once, the area is 272 square units. After you zoom in a second time, the area is 136 square units. a) Write an equation that can be used to find the area after zooming in n times. b) What is the viewable area after you zoom in five times?Group Challenge:Find the 8th term of a geometric sequence where a2 = 20 and r = 5? Explain the method you used to arrive at your answer.Lesson Summary: The ratio of successive terms in a geometric sequence is called the ________________________________. The explicit formula for a geometric sequence allows you to find the nth term of the sequence by substituting the values of ________ (first term) and ________ (common ratio) in the equation an = _________________.Problem Set:1. Find the common ratio of each of the following geometric sequences. Then write the explicit formula for each.a) 2, 6, 18, 54, ... b) 135, 45, 15, 5, ... c) 7, -14, 28, -56, ...2. a) Write an equation for the nth term of the geometric sequence. b) Using the equation, find a6.480060010350500a) 3, 6, 12, 24, ... b) 0.375, 3, 24, 192, ... c) 3. Given the following geometric sequence: 128, 32, 8, 2, 0.5, …a) Write an equation to find the nth term. b) Find the 8th term.4. Given the following geometric sequence: a) Write an equation to find the nth term. b) Find the 7th term. 2286000005. 6. In a geometric sequence the first term is 5 and the second term is 20, which of the following is the fifth term? (1) 65 (3) 80 (2) 1,280 (4) 5,1207. The table to the right shows the value of a car over a three year period after it had been purchased.52578004889500(a) Write an explicit formula that represents the sequence.(b) How much will the car be worth after 8 years? Round your answer to the nearest cent.(c) After how many years will the car have a value of approximately $3,000?(d) What was the purchase price of the car?(e) Would it be reasonable to use this model to predict the number of years it would take for the car's value to decline to about $100? Explain your reasoning.8. Michael is sick with the flu but he still comes to school on Monday. He arrives at 8am and by 9am (Hour 1), Michael has already infected two of his friends, Joe and Lia. By 10am (Hour 2), Joe has infected two of his friends, Bill and Ted, and Lia has infected two of her friends, Jenny and Kiara. a) If each person with the flu infects two other people in each hour, how many students are infected by 3pm (Hour 7)? Complete the table and graph the points on the grid below.434340015620900b) Does this situation represent an arithmetic or geometric sequence? c) Write an explicit formula to represent the sequence. d) Graph the sequence. Is it a picture of a line?9. What is the common ratio of the geometric sequence shown below?1)2)23)4)10. The common ratio of the sequence is1)2)3)4)11. What is the common ratio of the geometric sequence whose first term is 27 and fourth term is 64?1)2)3)4)12. The men’s U.S. Open tennis tournament is held annually in Flushing Meadow in NYC. In the first round of the tournament, 64 matches are played. In each successive round, the number of matches played decreases by one- half.Write the rule for the number of matches played in the nth round. For what values of n does this rule make sense?13. In 1990 factory sales of cell phones in the U.S. totaled $118 million. From 1990 through 1996, the sales increased by 20% per year.a) Write a rule for cell phone sales (in millions of dollars) in terms of the year. (Let n = 1 represent 1990) b) What did factory sales of pages total in 1992? c) When did factory sales of cell phones reach $300 million?14. On Monday, the first day of a flu epidemic, three employees of a company were absent. Throughout theweek, absences mounted geometrically, peaking at 48 employees on Friday. How many employees were absenton Tuesday, Wednesday and Thursday?15. Records at Danbury Hospital show 2, 10 and 50 new cases of chicken pox were reported for 3 consecutivedays. Assuming that the number of new cases continues to increase geometrically, how many new cases will bereported on the 5th day?Name ___________________________Exit SlipCommon Core Algebra Unit 12: Sequences 3/1/17Lesson 3: Geometric Sequences (Explicit)Objective: SWBAT identify a geometric sequence and apply the explicit formula to situations.Suppose you deposit one cent into your bank account on the first day of December. Each day in December after that, you deposit twice as much as on the previous day. Write an explicit formula to model the situation.Use your formula to determine how much money will be in the account on the 25th of December?Name ___________________________Exit SlipCommon Core Algebra Unit 12: Sequences 3/1/17Lesson 3: Geometric Sequences (Explicit)Objective: SWBAT identify a geometric sequence and apply the explicit formula to situations.Suppose you deposit one cent into your bank account on the first day of December. Each day in December after that, you deposit twice as much as on the previous day. Write an explicit formula to model the situation.Use your formula to determine how much money will be in the account on the 25th of December? ................
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