Standard Accessed: Students will analyze sequences, find sums of series, and use recursive rules.

Warm-up Check Find the common difference or common ratio for each sequence. 1. 5, 10, 15, 20, … d = 5 2.8, 4, 0, -4, … 3.216, -36, 6, -1, … 4.99, 200, 301, 402, … d = -4 d = 101

Big Idea How do you write a recursive rule for an arithmetic sequence and for a geometric sequence? By writing the first term and relating each other term to the term that precedes it.

Vocabulary Involves the repeated composition of a function f with itself. The result of one iteration is f(f(x)).

Evaluate Recursive Rules EXAMPLE 1 SOLUTION Write the first six terms of the sequence. (a) -2, 1, 4, 7, 10, 13 (b) 32, 16, 8, 4, 2, 1

Write Recursive Rules EXAMPLE 2 SOLUTION Write a recursive rule for the sequence.

Write Recursive Rules EXAMPLE 3 SOLUTION Write a recursive rule for the sequence.

Ryan’s Experiments: EXAMPLE 4 Solve a real life multi-step problem After the 5 th day there are 118 mosquitoes. The number decreases and stabilizes at 118 mosquitoes per day.

Iterate a function EXAMPLE 5 SOLUTION 1 st three iterates: 2, 7, 32 What is a recursive rule for the sequence?

Lesson 7.5 Use Recursive Rules with Sequences and Functions Homework: Honors – Homework Academic – Homework