Squares Inside Squares
Sequences
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Objective
Students use the TI-92 to generate a sequence by determining the areas of squares
inscribed in squares. They then write this sequence using the recursive form and the
explicit form for the sequence.
Overview of the Lesson
In this lesson, students explore another geometric pattern as they investigate the
pattern determined by the areas of squares inscribed in squares formed by joining
the midpoints of the sides of the previous square. The sequence generated is a
simple geometric one. One special feature of this lesson is the use of the TI-92,
which is used to generate the data. Students generate both the explicit and recursive
forms for the sequence. At the algebra I level, students do not need the formal
notation, but algebra I students are very capable of exploring the pattern, plotting the
model, and describing how to generate the sequence.
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