Lesson 7

Representing More Sequences

The practice problem answers are available at one of our IM Certified Partners

Problem 1

Here is the recursive definition of a sequence: \(f(1) = 10, f(n) = f(n-1) - 1.5\) for \(n\ge2\).

  1. Is this sequence arithmetic, geometric, or neither?
  2. List at least the first five terms of the sequence.
  3. Graph the value of the term \(f(n)\) as a function of the term number \(n\) for at least the first five terms of the sequence.

Problem 2

An arithmetic sequence \(k\) starts 12, 6, . . .

  1. Write a recursive definition for this sequence.
  2. Graph at least the first five terms of the sequence.

Problem 3

An arithmetic sequence \(a\) begins 11, 7, . . .

  1. Write a recursive definition for this sequence using function notation.
  2. Sketch a graph of the first 5 terms of \(a\).
  3. Explain how to use the recursive definition to find \(a(100)\). (Don't actually determine the value.)
(From Algebra2, Unit 1, Lesson 6.)

Problem 4

A geometric sequence \(g\) starts 80, 40, . . .

  1. Write a recursive definition for this sequence using function notation.
  2. Use your definition to make a table of values for \(g(n)\) for the first 6 terms.
  3. Explain how to use the recursive definition to find \(g(100)\). (Don't actually determine the value.)
(From Algebra2, Unit 1, Lesson 6.)

Problem 5

Match each recursive definition with one of the sequences.

(From Algebra2, Unit 1, Lesson 5.)

Problem 6

For each sequence, decide whether it could be arithmetic, geometric, or neither. 

  1. 25, 5, 1, . . .
  2. 25, 19, 13, . . .
  3. 4, 9, 16, . . .
  4. 50, 60, 70, . . .
  5. \(\frac{1}{2},\) 3, 18, . . .

For each sequence that is neither arithmetic nor geometric, how can you change a single number to make it an arithmetic sequence? A geometric sequence?

(From Algebra2, Unit 1, Lesson 3.)