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Algebra 1

4.17.5 Practice

Algebra 14.17.5 Practice
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Complete the following questions to practice the skills you have learned in this lesson.

For questions 1 – 3, match each sequence with one of the definitions. Note that only the part of the definition showing the relationship between the current term and the previous term is given so as not to give away the solutions.

  1. 6, 12, 18, 24
  1. d ( n ) = d ( n − 1 ) + 20
  2. c ( n ) = c ( n − 1 ) + 6
  3. b ( n ) = 1 2 b ( n − 1 )
  4. a ( n ) = 7 ⋅ a ( n − 1 )
  1. 2, 14, 98, 686
  1. d ( n ) = d ( n − 1 ) + 20
  2. c ( n ) = c ( n − 1 ) + 6
  3. b ( n ) = 1 2 b ( n − 1 )
  4. a ( n ) = 7 ⋅ a ( n − 1 )
  1. 160, 80, 40, 20
  1. d ( n ) = d ( n − 1 ) + 20
  2. c ( n ) = c ( n − 1 ) + 6
  3. b ( n ) = 1 2 b ( n − 1 )
  4. a ( n ) = 7 ⋅ a ( n − 1 )
For questions 4 – 5, select the first five terms of each sequence. Determine whether each sequence is arithmetic, geometric, or neither.
  1. a ( 1 ) = 7 , a ( n ) = a ( n − 1 ) − 3 for n ≥ 2 .
  1. 7, 4, 1, -2, -5, arithmetic
  2. 7, -21, 63, -189, arithmetic
  3. 7, -21, 63, -189, geometric
  4. 7, 4, 1, -2, -5, geometric
  1. c ( 1 ) = 3 , c ( n ) = 10 ⋅ c ( n − 1 ) for n ≥ 2 .
  1. 3, 13, 23, 33, 43, arithmetic
  2. 3, 13, 23, 33, 43, geometric
  3. 3, 30, 300, 3000, 30000, geometric
  4. 3, 30, 300, 3000, 30000, arithmetic
For questions 6 – 8, match each sequence with one of the recursive definitions. Note that only the part of the definition showing the relationship between the current term and the previous term is given so as not to give away the solutions.
  1. 3, 15, 75, 375
  1. d ( n ) = d ( n − 1 ) + n − 1
  2. c ( n ) = 5 ⋅ c ( n − 1 )
  3. b ( n ) = b ( n − 1 ) − 4
  4. a ( n ) = 1 3 ⋅ a ( n − 1 )
  1. 18, 6, 2, 2 3
  1. d ( n ) = d ( n − 1 ) + n − 1
  2. c ( n ) = 5 ⋅ c ( n − 1 )
  3. b ( n ) = b ( n − 1 ) − 4
  4. a ( n ) = 1 3 ⋅ a ( n − 1 )
  1. 17, 13, 9, 5
  1. d ( n ) = d ( n − 1 ) + n − 1
  2. c ( n ) = 5 ⋅ c ( n − 1 )
  3. b ( n ) = b ( n − 1 ) − 4
  4. a ( n ) = 1 3 ⋅ a ( n − 1 )
  1. An arithmetic sequence k starts 12, 6, . . . and is represented by the graph below.

Which of the following is a recursive definition for sequence k when n ≥ 2 ?

  1. k ( 1 ) = 12 , 6 ⋅ k ( n ) = k ( n − 1 )
  2. k ( 1 ) = 12 , k ( n ) = k ( n − 1 ) + 6
  3. k ( 1 ) = 12 , k ( n ) = k ( n − 1 ) − 6
  4. k ( 1 ) = 12 , k ( n ) = k ( n ) − 6
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