Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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Concept explainers

Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
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Question
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Chapter 3.6, Problem 30PPS

a.

To determine

To determine the function to represent the sequence.

a.

Expert Solution
Check Mark

Answer to Problem 30PPS

  f(n)=−11n+292

Explanation of Solution

Given:

Sequence:

  281,270,250,248,...

Formula used:

nth term of any arithmetic progression is given by the formula:

  tn=a+(n−1)d

  tn= nth term

  a= The first term of the arithmetic progression

  d= The common difference of the arithmetic progression

Calculation:

The common difference of the arithmetic progression is:

  270−281=−11

Applying above formula,

  ⇒an=a+(n−1)d

  ⇒an=281+(n−1)(−11)  [∵a=281&d=−11]

  ⇒an=281−11n+11⇒an=−11n+292

So, the nth term of the sequence is −11n+292.

Conclusion:

The required function of the sequence is f(n)=−11n+292 .

b.

To determine

To determine the weight of each year book.

b.

Expert Solution
Check Mark

Answer to Problem 30PPS

  11 oz.

Explanation of Solution

Given:

Sequence:

  281,270,250,248,...

Calculation / Explanation:

The common difference of the arithmetic progression is:

  270−281=−11

So, the weight decreases by 11 oz every time when a book is taken out.

Conclusion:

So, the common difference represents the weight of each year book, i.e. 11 oz.

c.

To determine

To determine the number of year books.

c.

Expert Solution
Check Mark

Answer to Problem 30PPS

  25 books

Explanation of Solution

Given:

The weight of the empty box: 17 ounces.

The weight of the full box: 292 ounces.

Calculation:

The weight of the books = The weight of the full box − The weight of the empty box

  292−17=275

The number of year books = The total weight of the all books ÷ The weight of a single book

  275÷11=25

Conclusion:

So, there are total 25 books in the full box.

d.

To determine

To determine the domain and range of the function

d.

Expert Solution
Check Mark

Answer to Problem 30PPS

  D={1,2,3,4...}&R={281,270,259,248...}

Explanation of Solution

Given:

Sequence:

  281,270,250,248,...

Calculation:

The domain of the function is the numbers of year books.

The range of the function is the weight of the box contain the books.

So, the domain and range are respectively: D={1,2,3,4...}&R={281,270,259,248...}.

Conclusion:

Therefore, the domain and range are respectively: D={1,2,3,4...}&R={281,270,259,248...}.

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Chapter 3.6, Problem 29PPS
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Chapter 3.6, Problem 31PPS

Chapter 3 Solutions

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Ch. 3.1 - Prob. 1AGPCh. 3.1 - Prob. 1BGPCh. 3.1 - Prob. 2GPCh. 3.1 - Prob. 3GPCh. 3.1 - Prob. 4AGPCh. 3.1 - Prob. 4BGPCh. 3.1 - Prob. 5AGPCh. 3.1 - Prob. 5BGPCh. 3.1 - Prob. 5CGPCh. 3.1 - Prob. 1CYU
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Prob. 51PPSCh. 3.5 - Prob. 52HPCh. 3.5 - Prob. 53HPCh. 3.5 - Prob. 54HPCh. 3.5 - Prob. 55HPCh. 3.5 - Prob. 56HPCh. 3.5 - Prob. 57PFACh. 3.5 - Prob. 58PFACh. 3.5 - Prob. 59PFACh. 3.5 - Prob. 60PFACh. 3.5 - Prob. 61PFACh. 3.5 - Prob. 62PFACh. 3.5 - Prob. 63PFACh. 3.5 - Prob. 64PFACh. 3.6 - Prob. 1AGPCh. 3.6 - Prob. 1BGPCh. 3.6 - Prob. 2GPCh. 3.6 - Prob. 3AGPCh. 3.6 - Prob. 3BGPCh. 3.6 - Prob. 3CGPCh. 3.6 - Prob. 3DGPCh. 3.6 - Prob. 4AGPCh. 3.6 - Prob. 4BGPCh. 3.6 - Prob. 1CYUCh. 3.6 - Prob. 2CYUCh. 3.6 - Prob. 3CYUCh. 3.6 - Prob. 4CYUCh. 3.6 - Prob. 5CYUCh. 3.6 - Prob. 6CYUCh. 3.6 - Prob. 7CYUCh. 3.6 - Prob. 8PPSCh. 3.6 - Prob. 9PPSCh. 3.6 - Prob. 10PPSCh. 3.6 - Prob. 11PPSCh. 3.6 - Prob. 12PPSCh. 3.6 - Prob. 13PPSCh. 3.6 - Prob. 14PPSCh. 3.6 - Prob. 15PPSCh. 3.6 - Prob. 16PPSCh. 3.6 - Prob. 17PPSCh. 3.6 - Prob. 18PPSCh. 3.6 - Prob. 19PPSCh. 3.6 - Prob. 20PPSCh. 3.6 - Prob. 21PPSCh. 3.6 - Prob. 22PPSCh. 3.6 - Prob. 23PPSCh. 3.6 - Prob. 24PPSCh. 3.6 - Prob. 25PPSCh. 3.6 - Prob. 26PPSCh. 3.6 - Prob. 27PPSCh. 3.6 - Prob. 28PPSCh. 3.6 - Prob. 29PPSCh. 3.6 - Prob. 30PPSCh. 3.6 - Prob. 31PPSCh. 3.6 - Prob. 32HPCh. 3.6 - Prob. 33HPCh. 3.6 - Prob. 34HPCh. 3.6 - Prob. 35HPCh. 3.6 - Prob. 36HPCh. 3.6 - Prob. 37PFACh. 3.6 - Prob. 38PFACh. 3.6 - Prob. 39PFACh. 3.6 - Prob. 40PFACh. 3.6 - Prob. 41PFACh. 3.6 - Prob. 42PFACh. 3.6 - Prob. 43PFACh. 3.7 - Prob. 1GPCh. 3.7 - Prob. 2GPCh. 3.7 - Prob. 3GPCh. 3.7 - Prob. 4GPCh. 3.7 - Prob. 1CYUCh. 3.7 - Prob. 2CYUCh. 3.7 - Prob. 3CYUCh. 3.7 - Prob. 4CYUCh. 3.7 - Prob. 5CYUCh. 3.7 - Prob. 6CYUCh. 3.7 - Prob. 7CYUCh. 3.7 - Prob. 8PPSCh. 3.7 - Prob. 9PPSCh. 3.7 - Prob. 10PPSCh. 3.7 - Prob. 11PPSCh. 3.7 - Prob. 12PPSCh. 3.7 - Prob. 13PPSCh. 3.7 - Prob. 14PPSCh. 3.7 - Prob. 15PPSCh. 3.7 - Prob. 16PPSCh. 3.7 - Prob. 17PPSCh. 3.7 - Prob. 18PPSCh. 3.7 - Prob. 19PPSCh. 3.7 - Prob. 20PPSCh. 3.7 - Prob. 21PPSCh. 3.7 - Prob. 22PPSCh. 3.7 - Prob. 23PPSCh. 3.7 - Prob. 24PPSCh. 3.7 - Prob. 25PPSCh. 3.7 - Prob. 26PPSCh. 3.7 - Prob. 27PPSCh. 3.7 - Prob. 28PPSCh. 3.7 - 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