Page 163 - IM_Algebra2_FL Print Sample.pdf

Student Task Statement
1. Describe how the pattern grows.
2. Find a formula for the number of circles in stage .
Student Response
Sample response:
1. Each stage has one more square and three more circles than the one before. 2. Stage has circles or for
Student Lesson Summary
Situations can lead to geometric sequences, arithmetic sequences, and sequences that are neither geometric nor arithmetic.
For example, here is a pattern of black squares surrounded by white squares, growing in stages.
The number of white squares in each stage grows (8, 13, 18. . .), with 5 more white squares each time. Since the same number of squares is added each time, the number of white squares form an arithmetic sequence. As a closed form de nition, , where
is the number of white squares in stage .
Situations leading to geometric sequences include population growth and scaling, such as the sequence for the area of the th piece of paper in a previous lesson.
Not all sequences are geometric or arithmetic, so many situations lead to sequences that are neither geometric nor arithmetic. For example, consider these patterns of dots, with a new row of dots introduced in each stage:
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Teacher Guide Algebra