i.
To calculation: The rule for
The Sierpinski carpet is a fractal created using squares. The process involves removing smaller squares from larger squares. First. divide a large square into nine congruent squares. Remove the center square. Repeat these steps for each smaller square, as shown below. Assume that each side of the initial square is one unit long.
The required rule is
Given information:
The given terms are
Calculation:
The number of squares removed at the first stage
The number of squares removed at the second stage
It is given that
The general formula for a geometric sequence is
Put the value of
Therefore, the required rule
The total number of squares removed through stage
Put the value of
ii.
To identify: The rule for b. Then find the remaining area of the original square after stage 12. Let b, be the remaining area of the original square after the nth stage.
The rule of
Explanation:
Consider the given sequence.
After the first stage the remaining area is
After the second stage the remaining area is
Observing this, it can conclude that the rule is
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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