a.
To identify: The model for the number of yellow folders
The model for the number of yellow folders is
Given information:
The given image is shown below:
Explanation:
Consider the given image.
There is 1 yellow folder in first step.
There are 5 yellow folders in second step.
There are 9 yellow folders in the third step.
So, the required sequence is: 1, 5, 9, …
It can be observed that each term is increase by 4 so the progression is the arithmetic with common difference 4.
The formula for the nth term of arithmetic progression is:
The model for the number of yellow folders is
b.
To identify: Model for the number of green folders
The model for the number of green folders is
Given information:
The given image is shown below:
Explanation:
Consider the given image.
There is 0 green folder in first step.
There are 4 green folders in second step.
There are 16 green folders in the third step.
So, the required sequence is: 0, 4, 16, …
Each term is the square of even terms, so the nth term is:
The model for the number of green folders is
c.
To identify: A model for the ratio of
The required model is
Given information:
The model for the number of yellow folders is
The model for the number of green folders is
Explanation:
Consider the given information.
The model for the number of yellow folders is
The model for the number of green folders is
Put
Thus, the ratio of yellow and green folders in the 4th step is 13:36.
So, total there must be
Now observe the image in first stage there is only one folder.
In second stage there are 9 folders which is
In third stage there are 25 folders which is
Thus, in fourth stage there must be 49 folders which is
Hence, verified.
Chapter 8 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education