i.
To identify: The rule for the number of visible blocks in the nth layer where n=1 represents the front layer.
Sol LeWitt's sculpture Four-Sided Pyramid in the National Gallery of Art Sculpture Garden is made of concrete blocks. As shown in the diagram, each layer has 8 more visible blocks than the layer in front of it.
The required rule is
Given information:
Given figure is:
Explanation:
Consider the given sequence.
The general formula for an arithmetic sequence is
Fist note that the differences of visible blocks between two layers are the same, so it the numbers of visible blocks in layers form an arithmetic sequence.
Each layer has
The number of visible blocks in the first layer is
Now, let's determine the
Put the value of
ii.
To calculate: How many of the pyramid's blocks are visible? When you view the pyramid from one corner, a total of 12 layers are visible.
Therefore, there are
Given information:
The given terms are
Calculation:
Consider the given sequence.
It is given that
Put the value of
The general sum formula for a arithmetic sequence is
Put the value of
Therefore, there are
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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