1. Recursive Routines Algebra 1

2. Recursive Routines An ordered list of numbers defined by a starting value and a rule An ordered list of numbers defined by a starting value and a rule The starting value is the first number of a sequence and it is represented by f(0) The starting value is the first number of a sequence and it is represented by f(0) The rule is an operation that is being applied at each step of the sequence The rule is an operation that is being applied at each step of the sequence Example: f(0) = 2, rule = +3 Example: f(0) = 2, rule = +3 2, 5, 8, 11, 14, 17, 20…. 2, 5, 8, 11, 14, 17, 20….

3. Recursive Routine You generate a recursive routine by: You generate a recursive routine by: Applying the rule to the starting value and any resulting number Applying the rule to the starting value and any resulting number Example Example f(0) = 10, Rule = - 3 f(0) = 10, Rule = - 3 10 – 3 = 7, 7 – 3 = 4, 4 – 3 = 1, 1 – 3 = -2, …. 10 – 3 = 7, 7 – 3 = 4, 4 – 3 = 1, 1 – 3 = -2, …. 10, 7, 4, 1, -2…. 10, 7, 4, 1, -2…. f(0)f(1)f(2)f(3)f(4)

4. Recursive Routine To find the starting value (f(0)) and the rule, find the pattern in the given sequence. To find the starting value (f(0)) and the rule, find the pattern in the given sequence. Use critical thinking skills and investigate/solve for the rule. Use critical thinking skills and investigate/solve for the rule. Example: Example: 7, 12, 17, 22, 27, 32, 37, 42, 47, 52 +5 f(0) = 7, Rule = +5

5. Recursive Routine Example 1 Example 1 5, 1, -3, -7, -11, -15, -19, -23, -27, -31 f(0) = 5, Rule = -4

6. Recursive Routine Example 3 Example 3 -7, -18, -29, -40, -51, -62, -73, -84, -95 f(0) = -7, Rule = -11

7. Calculator Notes For basic recursions on your calculators: * Enter the Starting Value, and hit enter. * Next, type in the rule, and hit enter again to get your second term. * After this, each subsequent push of the enter key will return the next terms in the sequence. Remember to keep track of the number of enters.

8. Recursive Routine Finding the nth term Finding the nth term What is the 15th term in the sequence? What is the 15th term in the sequence? Use your calculator! Use your calculator! 5, 1, -3, -7, -11, -15, -19, -23, -27, -31 f(0) = 5, Rule = -4 f(15) = -59

9. Recursive Routine Finding the nth term Finding the nth term What is the 15th term in the sequence? What is the 15th term in the sequence? f(15) = -172 -7, -18, -29, -40, -51, -62, -73, -84, -95 f(0) = -7, Rule = -11

10. Recursive Routine Write the first six terms in the sequence using the information given: Write the first six terms in the sequence using the information given: f(0) = 3 f(0) = 3 Rule = + 4 Rule = + 4 f(0) = 101 f(0) = 101 Rule = -.5 Rule = -.5 3, 7, 11, 15, 19, 23 101, 100.5, 100, 99.5, 99, 98.5

11. Recursive Routine State the starting value and rule for each sequence: State the starting value and rule for each sequence: 5, 10, 15, 20, 25… 5, 10, 15, 20, 25… -1, 1, -1, 1, -1… -1, 1, -1, 1, -1… f(0) f(0) = 5 Rule = +5 f(0) f(0) = -1 Rule = × (-1)