Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
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Expert Solution & Answer
Chapter 7.2, Problem 63PS
Solution
i.
To identify: . The rule for the number of cells in the nth ring.
HONEYCOMBS Domestic bees make their honeycomb by starting with a single hexagonal cell, then forming ring after ring of hexagonal cells around the initial cell, as shown. The numbers of cells in successive rings form an arithmetic sequence.
The required rule is
Given information:
The given image is:
Explanation:
Consider the given sequence.
The general formula for an arithmetic sequence is
The initial cell has 1 hexagonal cell
On the second image, can see that the initial cell and the first ring are combined to form one ring. It is made up of seven hexagonal cells. So, by subtracting one hexagonal cell or initial cell, we can conclude that the first ring is composed of six hexagonal cells.
Now, observe the third part of picture. There are initial cell, the first and the second ring. Thus, the second ring is made
hexagonal cells.
Therefore, the
ii.
To calculate: The total number of cells in the honeycomb after the 9th ring is formed?
Given information:
The given terms are
Calculation:
Consider the given sequence.
It is given that
The general sum formula for a arithmetic sequence is
Put the value of
Therefore after
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
Ch. 7.1 - Prob. 1GPCh. 7.1 - Prob. 2GPCh. 7.1 - Prob. 3GPCh. 7.1 - Prob. 4GPCh. 7.1 - Prob. 5GPCh. 7.1 - Prob. 6GPCh. 7.1 - Prob. 7GPCh. 7.1 - Prob. 8GPCh. 7.1 - Prob. 9GPCh. 7.1 - Prob. 10GP
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