Page 120 - IM_Algebra2_FL Print Sample.pdf

Example sequence: 160, 40, 10, 2.5, . . .
Common ratio:
Recursive de nition:
5.4 One More On Top
Cool Down: 5 minutes
Student Task Statement
Example sequence: 9, 5, 1, -3, . . .
Common di erence: -4
Recursive de nition:
A sequence has the recursive de nition for . 1. Explain how you know .
2. Write the rst ve terms of the sequence, starting with .
Student Response
1. Sample response: Substitute into the de nition. 2. 0, 2, 5, 9, 14
Student Lesson Summary
A recursive de nition of a sequence states how to calculate each term of the sequence based on the previous term, along with any necessary initial conditions.
Here’s a sequence: 6, 10, 14, 18, 22, . . . This is an arithmetic sequence, where each term is 4 more than the previous term. In function notation, that statement is written
. Here, is the term, is the previous term, and + 4 represents the change from the previous term.
A recursive de nition also must say what the rst term is. Without that, there would be no way of knowing if the sequence de ned by started with 6 or 91 or any other number.
Here, one possible initial condition is . (It is also acceptable to number the terms starting with 1, using but in this course we will typically start with 0.)
Combining this information gives the recursive de nition: and for .
Unit 1
Lesson 5: Recursive De nitions
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