Warm-Up Study the patterns below to determine the next five numbers in each sequence. You may use the calculator to check your answers. 2, 4, 6, 8, 10...

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Warm-Up Study the patterns below to determine the next five numbers in each sequence. You may use the calculator to check your answers. 2, 4, 6, 8, 10... 5, 10, 15, 20, 25... 3, 6, 9, 12, 15… 10, 20, 30, 40, 50… 11, 22, 33, 44, 55… http://www.online-stopwatch.com/

Recursive patterns

Vocabulary Recursive equation: An equation that shows how to calculate the value of the next term from the value of the current term. Sequence: A list of numbers where each term is based on the previous terms using a set pattern or rule.

Vocabulary Domain: The set of all inputs. (x-values) Range: The set of all outputs. (y-values) TERM NUMBER VALUE

Now-Next form of Recursive Equations Start = _____________ What is the pattern? _________________ Now – Next form: ___________________ Start = _____________ What is the pattern? _________________ Now – Next form: ___________________

You Try!

Geometric Now-Next Start = _____________ Now – Next form: ___________________

You Try! Start = _____________ Now – Next form: ___________________

Iterating Functions on the Graphing Calculator

Iterating Functions on the Graphing Calculator Example: List the first six values generated by the recursive routine below. Then write the routine as a NOW-NEXT equation. First six values: ___________________________________ Now – Next form: ___________________________________

Iterating Functions on the Graphing Calculator Example: List the first six values generated by the recursive routine below. Then write the routine as a NOW-NEXT equation. First six values: ___________________________________ Now – Next form: ___________________________________

You Try! First six values: ________________________________ 1) Find the first 5 terms of the sequence for NEXT = –6 • NOW + 12 when the initial value is 2. First five values: ________________________ 2) List the first six values generated by the recursive routine below. Then write the routine as a NOW-NEXT equation. First six values: ________________________________ Now – Next form: ________________________________