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Algebra 2B Day 30 11.1 Patterns Daily Openers Go over and collect homework 11.1 Patterns sequence – ordered list of numbers term – each number in a sequence Ex. You drop a super ball from a height of 12 feet. If the ball rebounds to 80% of its previous height, how high will the ball rebound after its 5th bounce? recursive formula – where a term in a sequence is defined by relating it to the previous term. Ex. Describe the pattern, and write a recursive formula for the sequence: (a) 2, 5, 8, 11, 14, … (b) 5, 10, 20, 40, … (c) 1, -6, 36, -216, … Ex. In the sequence: 33, 29, 25, 21, 17, …, a1 represents the 1st term, a2 represents the 2nd term, a3 represents the 3rd term, and so on. Find a7, a10, and a14 Ex. For the recursive formula: an 2an1 3 , where Ex. For the recursive formula: a n a1 4 , find a 5 . 2 a n 1 , where a1 18 , find a 6 . 3 explicit formula – expresses the nth term in terms of n. – you don’t need to know the previous term to find the nth term. Ex. For the explicit formula: a n 4n 5 , find Ex. For the explicit formula: an 3n n , find 2 a 20 a11 Homework – page 603 #1–41 all, 46, 48 Daily Openers – Find the next three terms in the pattern: 1. 1, 1, 2, 3, 5, 8, ____ , ____ , ____ 1 1 1 2. 1, , , 1 , -2, ____ , ____ , ____ 4 4 2 3. 0, 8, 27, 64, ____ , ____ , ____ 1 1 3 6 4. Simplify: 2 3 4n 2 2n 3 5. Solve: 2 n 9 n3 n3