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Algebra 1

4.18.2 Identifying Domain for a Function

Algebra 14.18.2 Identifying Domain for a Function

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Activity

A Sierpinski triangle can be created by starting with an equilateral triangle, breaking the triangle into 4 congruent equilateral triangles, and then removing the middle triangle. Starting from a single black equilateral triangle:

Four triangles show the stages of creating a Sierpinski triangle: the first is solid black, and each subsequent triangle has progressively smaller white triangles cut out, forming a fractal pattern.

1. Let S S be the number of black triangles in Step n n . Define S ( n ) S ( n ) recursively.

2. Andre and Lin are asked to write an equation for S S that isn’t recursive. Andre writes S ( n ) = 3 n S ( n ) = 3 n for n 0 n 0 , while Lin writes S ( n ) = 3 n 1 S ( n ) = 3 n 1 for n 1 n 1 . Whose equation do you think is correct? Be prepared to show your reasoning.

Video: Learning About Sierpinski’s Triangle

Watch the following video to learn more about how to write a pattern as an nth term.

Are you ready for more?

Extending Your Thinking

Here is a geometric sequence. Find the missing terms.

3, ____, 6, ____, 12, ____, 24

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