Lesson 6 Practice Problems 4. Write the first five terms of each sequence. 1 . An arithmetic sequence a starts 2 , 5 , ... a. a(1) = 1, a(n) = 3 . a(n - 1), n 2 2 a. Write a recursive definition for this sequence using function notation. b. b ( 1 ) = 1, b(n) = -2 + b(n - 1), n >2 c. c(1) = 1, c(n) = 2 . c(n - 1) + 1, n >2 b. Use your definition to make a table of values for a(m) and find a(6). d. d(1) = 1, d(n) = d(n - 1)2 + 1, n>2 e. f(1) = 1, f(n) = f(n - 1) + 2n - 2, n 2 2 2 . A geometric sequence & starts 1 , 3 , ... (From Unit 1, Lesson 5.) a. Write a recursive definition for this sequence using function notation. 5. A sequence has f(1) = 120, f(2) = 60. a. Determine the next 2 terms if it is an arithmetic sequence, then write a b. Sketch a graph of the first 5 terms of g. recursive definition that matches the sequence in the form f(1) = 120, f(n) = f(n - 1) +_forn > 2. b. Determine the next 2 terms if it is a geometric sequence, then write a recursive definition that matches the sequence in the form C. Explain how to use the recursive definition to determine g(30). (Don't actually f(1) = 120, f(n) = _. f(n - 1) forn 2 2. determine the value.) (From Unit 1, Lesson 5.) 6. One hour after an antibiotic is administered, a bacteria 3. Match each sequence with one of the recursive definitions. Note that only the part of population is 1,000,000. Each following hour, it decreases by a number the definition showing the relationship between the current term and the previous factor of 7. of population term is given so as not to give away the solutions. hours a. Complete the table with the bacteria population at the A. 3, 15, 75, 375 1. a(n) = = . a(n - 1) given times. 1,000,000 NIS 2. b(n) = b(n - 1) - 4 b. Do the bacteria populations make a geometric sequence? V Explain how you know. C. 1, 2, 4, 7 3. c(n) = 5 . c(n - 1) D. 17, 13, 9, 5 4. d(n) = d(n - 1) +n - 1 (From Unit 1, Lesson 5.) (From Unit 1, Lesson 2.) Unit 1 Lesson 6 Practice Problems