Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
2nd Edition
ISBN: 9780076602919
Author: McGraw-Hill Education
Publisher: McGraw-Hill Education
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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 write: a function to represent the sequence.

a)

Expert Solution
Check Mark

Answer to Problem 30PPS

A function to represent the sequenceis f(n)=−11n+292 .

Explanation of Solution

Given:

An arithmetic sequence is given as:

281, 270, 259, 248, …

The sequence represents the total number of ounces the box weighs as each book is taken out.

Calculation:

Consider the given terms.

281, 270, 259, 248, …

Now, find the common difference of the sequence as shown:

  270−281=259−270=248−259=−11

The sequence is decreasing, so the common difference is positive: −11 .

Write the equation for the nth term of an arithmetic sequence using the first term 281 and common difference −11 .

  an=a1+(n−1)dan=281+(n−1)(−11)an=281−11n+11an=−11n+292

So, the function to represent the sequence is f(n)=−11n+292 .

b)

To determine

To find: the weight of each year book.

b)

Expert Solution
Check Mark

Answer to Problem 30PPS

The weight of each yearbook is 11 ounces.

Explanation of Solution

Given:

An arithmetic sequence is given as:

281, 270, 259, 248, …

The sequence represents the total number of ounces the box weighs as each book is taken out.

Calculation:

Consider the given terms.

281, 270, 259, 248, …

Now, find the common difference of the sequence as shown:

  270−281=259−270=248−259=−11

The sequence is decreasing, so the common difference is positive: −11 .

The weight decreases by 11 ounce every time a book is taken out, so the common difference represents the weight of each yearbook, or 11 ounces.

c)

To determine

To find: the number of yearbooks in a full box.

c)

Expert Solution
Check Mark

Answer to Problem 30PPS

The number of yearbooks in a full boxis 25.

Explanation of Solution

Given:

An arithmetic sequence is given as:

281, 270, 259, 248, …

The sequence represents the total number of ounces the box weighs as each book is taken out.

Empty box weight 17 ounces and full box weighs 292 ounces.

Calculation:

Consider the given terms.

281, 270, 259, 248, …

Now, subtract the weight of the empty box from the weight of the full box.

  292−17=275

Now, divide by the weight by 11 to get number yearbook

  275÷11=25

So, there are 25 books in a full box.

d)

To determine

To find: the domain and range of the function obtained in part (a).

d)

Expert Solution
Check Mark

Answer to Problem 30PPS

The domain of the function is {1,2,3,4,5,6,7,8,...,25} .

The range of the function is {281,27,259,248,...,17}

Explanation of Solution

Given:

An arithmetic sequence is given as:

281, 270, 259, 248, …

The sequence represents the total number of ounces the box weighs as each book is taken out.

Empty box weight 17 ounces and full box weighs 292 ounces.

Calculation:

Consider the given terms.

281, 270, 259, 248, …

Now, subtract the weight of the empty box from the weight of the full box.

  292−17=275

Now, divide by the weight by 11 to get number yearbook

  275÷11=25

So, there are 25 books in a full box.

The domain of the function is the number books. So, the domain is

  {1,2,3,4,5,6,7,8,...,25} .

The range of the function is weighs of books.

  {281,27,259,248,...,17}

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

Chapter 3 Solutions

Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)

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. 13MCQCh. 3 - Prob. 14MCQCh. 3 - Prob. 15MCQCh. 3 - Prob. 16MCQCh. 3 - Prob. 17MCQCh. 3 - Prob. 18MCQCh. 3 - Prob. 19MCQCh. 3 - Prob. 20MCQCh. 3 - Prob. 21MCQCh. 3 - Prob. 22MCQCh. 3 - Prob. 23MCQCh. 3 - Prob. 24MCQCh. 3 - Prob. 25MCQCh. 3 - Prob. 26MCQCh. 3 - Prob. 1SGRCh. 3 - Prob. 2SGRCh. 3 - Prob. 3SGRCh. 3 - Prob. 4SGRCh. 3 - Prob. 5SGRCh. 3 - Prob. 6SGRCh. 3 - Prob. 7SGRCh. 3 - Prob. 8SGRCh. 3 - Prob. 9SGRCh. 3 - Prob. 10SGRCh. 3 - Prob. 11SGRCh. 3 - Prob. 12SGRCh. 3 - Prob. 13SGRCh. 3 - Prob. 14SGRCh. 3 - Prob. 15SGRCh. 3 - Prob. 16SGRCh. 3 - Prob. 17SGRCh. 3 - Prob. 18SGRCh. 3 - Prob. 19SGRCh. 3 - Prob. 20SGRCh. 3 - Prob. 21SGRCh. 3 - Prob. 22SGRCh. 3 - Prob. 23SGRCh. 3 - Prob. 24SGRCh. 3 - Prob. 25SGRCh. 3 - Prob. 26SGRCh. 3 - Prob. 27SGRCh. 3 - Prob. 28SGRCh. 3 - Prob. 29SGRCh. 3 - Prob. 30SGRCh. 3 - Prob. 31SGRCh. 3 - Prob. 32SGRCh. 3 - Prob. 33SGRCh. 3 - Prob. 34SGRCh. 3 - Prob. 35SGRCh. 3 - Prob. 36SGRCh. 3 - Prob. 37SGRCh. 3 - Prob. 38SGRCh. 3 - Prob. 39SGRCh. 3 - Prob. 40SGRCh. 3 - Prob. 41SGRCh. 3 - Prob. 42SGRCh. 3 - Prob. 43SGRCh. 3 - Prob. 44SGRCh. 3 - Prob. 45SGRCh. 3 - Prob. 46SGRCh. 3 - Prob. 47SGRCh. 3 - Prob. 48SGRCh. 3 - Prob. 49SGRCh. 3 - Prob. 50SGRCh. 3 - Prob. 51SGRCh. 3 - Prob. 52SGRCh. 3 - Prob. 53SGRCh. 3 - Prob. 54SGRCh. 3 - Prob. 55SGRCh. 3 - Prob. 56SGRCh. 3 - Prob. 57SGRCh. 3 - Prob. 58SGRCh. 3 - Prob. 59SGRCh. 3 - Prob. 60SGRCh. 3 - Prob. 61SGRCh. 3 - Prob. 62SGRCh. 3 - Prob. 63SGRCh. 3 - Prob. 64SGRCh. 3 - Prob. 65SGRCh. 3 - Prob. 66SGRCh. 3 - Prob. 67SGRCh. 3 - Prob. 68SGRCh. 3 - Prob. 69SGRCh. 3 - Prob. 70SGRCh. 3 - Prob. 71SGRCh. 3 - Prob. 72SGRCh. 3 - Prob. 73SGRCh. 3 - Prob. 74SGRCh. 3 - Prob. 75SGRCh. 3 - Prob. 76SGRCh. 3 - Prob. 77SGRCh. 3 - Prob. 78SGRCh. 3 - Prob. 1PTCh. 3 - Prob. 2PTCh. 3 - Prob. 3PTCh. 3 - Prob. 4PTCh. 3 - Prob. 5PTCh. 3 - Prob. 6PTCh. 3 - Prob. 7PTCh. 3 - Prob. 8PTCh. 3 - Prob. 9PTCh. 3 - Prob. 10PTCh. 3 - Prob. 11PTCh. 3 - Prob. 12PTCh. 3 - Prob. 13PTCh. 3 - Prob. 14PTCh. 3 - Prob. 15PTCh. 3 - Prob. 16PTCh. 3 - Prob. 17PTCh. 3 - Prob. 18PTCh. 3 - Prob. 19PTCh. 3 - Prob. 20PTCh. 3 - Prob. 21PTCh. 3 - Prob. 22PTCh. 3 - Prob. 23PTCh. 3 - Prob. 24PTCh. 3 - Prob. 25PTCh. 3 - Prob. 26PTCh. 3 - Prob. 27PTCh. 3 - Prob. 1CRCh. 3 - Prob. 2CRCh. 3 - Prob. 3CRCh. 3 - Prob. 4CRCh. 3 - Prob. 5CRCh. 3 - Prob. 6CRCh. 3 - Prob. 7CRCh. 3 - Prob. 8CRCh. 3 - Prob. 9CRCh. 3 - Prob. 10CRCh. 3 - Prob. 11CRCh. 3 - Prob. 12CRCh. 3 - Prob. 13CRCh. 3 - Prob. 14CR

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