1. Lesson 8
Linear Equations
Recursive Routines

2. Warm-Up Write the first five non-zero multiples of 2.

3. Target: Write recursive routines and create recursive sequences.

4. Vocabulary
Recursive Sequence: Ordered list of numbers that begins with a start value. Each term in the sequence is generated by applying an operation to the term before it.
Recursive Routine: Described by stating the start value and the operation that is performed to get to the next term.

5. Example 1a For the recursive sequence, state the start value,
operation and next three terms.
8, 17, 26, 35, 44, …
Start value = 8
Operation = Add 9
Next three: 53, 62, 71

6. Example 1b For the recursive sequence, state the start value,
operation and next three terms.
6, 2, –2, –6, –10
Start value = 6
Operation = Subtract 4
Next three: –14, –18, –22

9. Example 2a Find the missing values in the sequence. Identify the
start value and the operation that must be performed to
arrive at the next term.
25, 19, 13, ___, 1, ___, ___
Start Value: 25
Operation: Subtract 6
Completed List: 25, 19, 13, 7, 1, −5, − 11

10. Example 2b Find the missing values in the sequence. Identify the start
value and the operation that must be performed to arrive
at the next term.
32, 45, ___, ___, 84, ___
Start Value: 32
Operation: Add 13
Completed List: 32, 45, 58, 71, 84, 97

11. Example 3a For the sequence, describe the recursive routine by giving
the starting value and operation. Give the 15th term.
35, 50, 65, 80
Start Value: 35
Operation: Add 15
15th Term: 245

12. Example 3b For the sequence, describe the recursive routine by giving
the starting value and operation. Give the 15th term.
10, 1, −8, −17
Start Value: 10
Operation: Subtract 9
15th Term: −116

13. Exit Problems Write the recursive routine for each sequence.
List the next two terms.
13, 16, 19, …
18, 17.5, 17, 16.5, …
Find the 8th term in the following sequence:
2, 9, 16, 23, …

14. Communication Prompt
What is something in your life that could be described by a recursive routine?