Recursive & Explicit Processes

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Presentation transcript:

Recursive & Explicit Processes Lesson 32

Objectives HSF-BF.2: Write arithmetic and geometric sequences both Recursively and with and explicit formula, use them to model situations, and translate between the two forms.

Example; writing terms of a sequence Write the first four terms of each sequence. a. a1 = 5; ak = –2(ak-1) + 6 Solution: a. The first five terms of the sequence given by a1 = 5; ak = –2(ak-1) + 6 a1 = 5 a2 = -2(5) + 6 = -4 a3 = -2(-4) + 6 = 14 a4 = -2(14) + 6 = -22 a5 = -2(-22) + 6 = 50 5, -4, 14, -22, 50, …

Example; writing terms of a sequence Write the first four terms of each sequence. b. a1 = 1; ak = (ak-1)2 + 2 Solution: b. The first five terms of the sequence given by a1 = 1; ak = (ak-1)2 + 2 a1 = 1 a2 = (1)2 + 2 = 3 a3 = (3)2 + 2 = 11 a4 = (11)2 + 2 = 123 a5 = (123)2 + 2 = 15,131 1, 3, 11, 123, 15131, …

Example; Recursive Formula c. Suppose you have the sequence: 5, 25, 125, 625, 3125, … Write a recursive formula for the sequence. Where does the sequence start? Start at 5 What happens in the sequence? Multiply by 5 Find a1. a1 = 5 Find ak. ak = 5(ak-1)

Example; Recursive Formula d. Suppose you have the sequence: 2, 5, 8, 11, 14, … Write a recursive formula for the sequence. Where does the sequence start? Start at 2 What happens in the sequence? Add by 3 Find a1. a1 = 2 Find ak. ak = (ak-1) + 3

#32: Recursive & Explicit Processes Questions? Summarize Notes Homework Google Classroom Quiz