Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Question
Chapter 12, Problem 1RCC

a.

To determine

Explain the meaning of sequence.

a.

Expert Solution
Check Mark

Answer to Problem 1RCC

A sequence is an enumerated collection of objects in which repetitions are allowed and order does matter, for example there are many types of sequence like arithmetic and geometric.

Explanation of Solution

Given information:

It is given in the question that, define the meaning of sequence.

A sequence is an enumerated collection of objects in which repetitions are allowed and order does matter, for example there are many types of sequence like arithmetic and geometric.

b.

To determine

Explain the meaning of an arithmetic sequence and also write the expression for the nth term of sequence.

b.

Expert Solution
Check Mark

Answer to Problem 1RCC

An arithmetic sequence is a sequence of the numbers such that the difference between the consecutive terms is constant and the expression for the nth term of sequence is an=a+(n1)d

Where,

  anisthenthtermaisthefirsttermnisthenumberoftermdisthecommandifference

Explanation of Solution

Given information:

It is given in the question that, to explain the meaning of arithmetic sequence and also write the expression for the nth term of arithmetic sequence.

An arithmetic sequence is a sequence of the numbers such that the difference between the consecutive terms is constant and the expression for the nth term of arithmetic sequence is an=a+(n1)d

Where,

  anisthenthtermaisthefirsttermnisthenumberoftermdisthecommandifference

c.

To determine

Explain the meaning of geometric sequence and also write the expression for the nth term of geometric sequence.

c.

Expert Solution
Check Mark

Answer to Problem 1RCC

A geometric sequence is a sequence of the numbers such that the difference ratio of the two consecutive terms is constant and the expression for the nth term of geometric sequence is an=arn1

Where,

  anisthenthtermaisthefirsttermnisthenumberoftermristhecommanratio

Explanation of Solution

Given information:

It is given in the question that, to explain the meaning of geometric sequence and also write the expression for the nth term of geometric sequence.

A geometric sequence is a sequence of the numbers such that the difference ratio of the two consecutive terms is constant and the expression for the nth term of geometric sequence is an=arn1

Where,

  anisthenthtermaisthefirsttermnisthenumberoftermristhecommanratio

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 12 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 12.1 - Prob. 11ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 13ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 15ECh. 12.1 - Prob. 16ECh. 12.1 - Prob. 17ECh. 12.1 - Prob. 18ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Prob. 22ECh. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Prob. 27ECh. 12.1 - Prob. 28ECh. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Prob. 31ECh. 12.1 - Prob. 32ECh. 12.1 - Prob. 33ECh. 12.1 - Prob. 34ECh. 12.1 - Prob. 35ECh. 12.1 - Prob. 36ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 40ECh. 12.1 - Prob. 41ECh. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 12.1 - Prob. 44ECh. 12.1 - Prob. 45ECh. 12.1 - Prob. 46ECh. 12.1 - Prob. 47ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 49ECh. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - Prob. 52ECh. 12.1 - Prob. 53ECh. 12.1 - Prob. 54ECh. 12.1 - Prob. 55ECh. 12.1 - Prob. 56ECh. 12.1 - Prob. 57ECh. 12.1 - Prob. 58ECh. 12.1 - Prob. 59ECh. 12.1 - Prob. 60ECh. 12.1 - Prob. 61ECh. 12.1 - Prob. 62ECh. 12.1 - Prob. 63ECh. 12.1 - Prob. 64ECh. 12.1 - Prob. 65ECh. 12.1 - Prob. 66ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 69ECh. 12.1 - Prob. 70ECh. 12.1 - Sigma Notation Write the sum using sigma notation....Ch. 12.1 - Prob. 72ECh. 12.1 - Prob. 73ECh. 12.1 - Prob. 74ECh. 12.1 - nth Term of a Sequence Find a formula for the nth...Ch. 12.1 - Prob. 76ECh. 12.1 - Compound Interest Julio deposits 2000 in a savings...Ch. 12.1 - Prob. 78ECh. 12.1 - Population of a City A city was incorporated in...Ch. 12.1 - Prob. 80ECh. 12.1 - Prob. 81ECh. 12.1 - Prob. 82ECh. 12.2 - An arithmetic sequence is a sequence in which the...Ch. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.2 - Prob. 11ECh. 12.2 - Prob. 12ECh. 12.2 - Prob. 13ECh. 12.2 - Prob. 14ECh. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - Prob. 17ECh. 12.2 - Prob. 18ECh. 12.2 - Prob. 19ECh. 12.2 - Prob. 20ECh. 12.2 - Prob. 21ECh. 12.2 - Prob. 22ECh. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Prob. 27ECh. 12.2 - Prob. 28ECh. 12.2 - Prob. 29ECh. 12.2 - Prob. 30ECh. 12.2 - Prob. 31ECh. 12.2 - Prob. 32ECh. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Prob. 35ECh. 12.2 - Prob. 36ECh. 12.2 - Prob. 37ECh. 12.2 - Prob. 38ECh. 12.2 - Prob. 39ECh. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Prob. 46ECh. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 49ECh. 12.2 - Prob. 50ECh. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.2 - Prob. 60ECh. 12.2 - Depreciation The purchase value of an office...Ch. 12.2 - Poles in a Pile Telephone poles are being stored...Ch. 12.2 - Salary Increases A man gets a job with a salary of...Ch. 12.2 - Drive-In Theater A drive-in theater has spaces for...Ch. 12.2 - Theater Seating An architect designs a theater...Ch. 12.2 - Prob. 66ECh. 12.2 - The Twelve Days of Christmas In the well-known...Ch. 12.2 - Prob. 68ECh. 12.3 - A geometric sequence is a sequence in which the...Ch. 12.3 - Prob. 2ECh. 12.3 - True or False? If we know the first and second...Ch. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prob. 8ECh. 12.3 - Prob. 9ECh. 12.3 - Prob. 10ECh. 12.3 - Prob. 11ECh. 12.3 - Prob. 12ECh. 12.3 - Prob. 13ECh. 12.3 - Prob. 14ECh. 12.3 - Prob. 15ECh. 12.3 - Prob. 16ECh. 12.3 - Prob. 17ECh. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 22ECh. 12.3 - Prob. 23ECh. 12.3 - Prob. 24ECh. 12.3 - Prob. 25ECh. 12.3 - Prob. 26ECh. 12.3 - Prob. 27ECh. 12.3 - Prob. 28ECh. 12.3 - Prob. 29ECh. 12.3 - Prob. 30ECh. 12.3 - Prob. 31ECh. 12.3 - Prob. 32ECh. 12.3 - Prob. 33ECh. 12.3 - Prob. 34ECh. 12.3 - Prob. 35ECh. 12.3 - Prob. 36ECh. 12.3 - Prob. 37ECh. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - Prob. 44ECh. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - Prob. 48ECh. 12.3 - Prob. 49ECh. 12.3 - Prob. 50ECh. 12.3 - Prob. 51ECh. 12.3 - Prob. 52ECh. 12.3 - Prob. 53ECh. 12.3 - Prob. 54ECh. 12.3 - Prob. 55ECh. 12.3 - Prob. 56ECh. 12.3 - Prob. 57ECh. 12.3 - Prob. 58ECh. 12.3 - Prob. 59ECh. 12.3 - Prob. 60ECh. 12.3 - Prob. 61ECh. 12.3 - Prob. 62ECh. 12.3 - Prob. 63ECh. 12.3 - Prob. 64ECh. 12.3 - Prob. 65ECh. 12.3 - Prob. 66ECh. 12.3 - Prob. 67ECh. 12.3 - Prob. 68ECh. 12.3 - Prob. 69ECh. 12.3 - Prob. 70ECh. 12.3 - Depreciation A construction company purchases a...Ch. 12.3 - Prob. 72ECh. 12.3 - Bouncing Ball A ball is dropped from a height of...Ch. 12.3 - Bacteria Culture A culture initially has 5000...Ch. 12.3 - Mixing Coolant A truck radiator holds 5 gal and is...Ch. 12.3 - Musical Frequencies The frequencies of musical...Ch. 12.3 - Bouncing Ball A ball is dropped from a height of 9...Ch. 12.3 - Prob. 78ECh. 12.3 - St. Ives The following is a well-known childrens...Ch. 12.3 - Prob. 80ECh. 12.3 - Bouncing Ball A certain ball rebounds to half the...Ch. 12.3 - Prob. 82ECh. 12.3 - Geometry A circular disk of radius R is cut out of...Ch. 12.3 - Prob. 84ECh. 12.3 - PROVE: Logarithms of a Geometric Sequence If a1,...Ch. 12.3 - Prob. 86ECh. 12.3 - Prob. 87ECh. 12.3 - Prob. 88ECh. 12.3 - Prob. 89ECh. 12.4 - An annuity is a sum of money that is paid in...Ch. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Annuity Find the amount of an annuity that...Ch. 12.4 - Annuity Find the amount of an annuity that...Ch. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Saving How much money should be invested monthly...Ch. 12.4 - Prob. 11ECh. 12.4 - Prob. 12ECh. 12.4 - Prob. 13ECh. 12.4 - Funding an Annuity A 55-year-old man deposits...Ch. 12.4 - Prob. 15ECh. 12.4 - Prob. 16ECh. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Mortgage Dr. Gupta is considering a 30-year...Ch. 12.4 - Prob. 20ECh. 12.4 - Prob. 21ECh. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Prob. 24ECh. 12.4 - Interest Rate John buys a stereo system for 640....Ch. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Interest Rate A man purchases a 2000 diamond ring...Ch. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.5 - Mathematical induction is a method of proving that...Ch. 12.5 - Prob. 2ECh. 12.5 - Prob. 3ECh. 12.5 - Prob. 4ECh. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Prob. 10ECh. 12.5 - Prob. 11ECh. 12.5 - Prob. 12ECh. 12.5 - Prob. 13ECh. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Prob. 16ECh. 12.5 - Prob. 17ECh. 12.5 - Prob. 18ECh. 12.5 - Prob. 19ECh. 12.5 - Prob. 20ECh. 12.5 - Prob. 21ECh. 12.5 - Prob. 22ECh. 12.5 - Prob. 23ECh. 12.5 - Prob. 24ECh. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Prob. 28ECh. 12.5 - Prob. 29ECh. 12.5 - Prob. 30ECh. 12.5 - Prob. 31ECh. 12.5 - Prob. 32ECh. 12.5 - Prob. 33ECh. 12.5 - Prob. 34ECh. 12.5 - Prob. 35ECh. 12.5 - Prob. 36ECh. 12.5 - Prob. 37ECh. 12.5 - Prob. 38ECh. 12.6 - An algebraic expression of the form a + b, which...Ch. 12.6 - Prob. 2ECh. 12.6 - The binomial coefficients can be calculated...Ch. 12.6 - Prob. 4ECh. 12.6 - Prob. 5ECh. 12.6 - Prob. 6ECh. 12.6 - Prob. 7ECh. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Prob. 11ECh. 12.6 - Prob. 12ECh. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Prob. 15ECh. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Prob. 18ECh. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - Prob. 24ECh. 12.6 - Prob. 25ECh. 12.6 - Prob. 26ECh. 12.6 - Prob. 27ECh. 12.6 - Prob. 28ECh. 12.6 - Prob. 29ECh. 12.6 - Prob. 30ECh. 12.6 - Prob. 31ECh. 12.6 - Prob. 32ECh. 12.6 - Prob. 33ECh. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Prob. 36ECh. 12.6 - Prob. 37ECh. 12.6 - Prob. 38ECh. 12.6 - Prob. 39ECh. 12.6 - Prob. 40ECh. 12.6 - Prob. 41ECh. 12.6 - Prob. 42ECh. 12.6 - Prob. 43ECh. 12.6 - Prob. 44ECh. 12.6 - Prob. 45ECh. 12.6 - Prob. 46ECh. 12.6 - Prob. 47ECh. 12.6 - Prob. 48ECh. 12.6 - Prob. 49ECh. 12.6 - Prob. 50ECh. 12.6 - Prob. 51ECh. 12.6 - Prob. 52ECh. 12.6 - Prob. 53ECh. 12.6 - Prob. 54ECh. 12.6 - Difference in Volumes of Cubes The volume of a...Ch. 12.6 - Probability of Hitting a Target The probability...Ch. 12.6 - Prob. 57ECh. 12.6 - Prob. 58ECh. 12.6 - Prob. 59ECh. 12 - Prob. 1RCCCh. 12 - Prob. 2RCCCh. 12 - Prob. 3RCCCh. 12 - Prob. 4RCCCh. 12 - Prob. 5RCCCh. 12 - Prob. 6RCCCh. 12 - Prob. 7RCCCh. 12 - Prob. 8RCCCh. 12 - Prob. 1RECh. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Prob. 40RECh. 12 - Prob. 41RECh. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Prob. 45RECh. 12 - Prob. 46RECh. 12 - Prob. 47RECh. 12 - Prob. 48RECh. 12 - Prob. 49RECh. 12 - Prob. 50RECh. 12 - Prob. 51RECh. 12 - Prob. 52RECh. 12 - Prob. 53RECh. 12 - Prob. 54RECh. 12 - Prob. 55RECh. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Prob. 58RECh. 12 - Prob. 59RECh. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - Prob. 64RECh. 12 - Prob. 65RECh. 12 - Prob. 66RECh. 12 - Prob. 67RECh. 12 - Prob. 68RECh. 12 - Prob. 69RECh. 12 - Prob. 70RECh. 12 - Prob. 71RECh. 12 - Prob. 72RECh. 12 - Prob. 73RECh. 12 - Prob. 74RECh. 12 - Prob. 75RECh. 12 - Prob. 76RECh. 12 - Prob. 77RECh. 12 - Prob. 78RECh. 12 - Prob. 79RECh. 12 - Prob. 80RECh. 12 - Prob. 81RECh. 12 - Prob. 82RECh. 12 - Prob. 83RECh. 12 - Prob. 1TCh. 12 - Prob. 2TCh. 12 - Prob. 3TCh. 12 - A geometric sequence begins 12,3,34,316,364,. (a)...Ch. 12 - The first term of a geometric sequence is 25, and...Ch. 12 - The first term of an arithmetic sequence is 10,...Ch. 12 - Prob. 7TCh. 12 - Write the expression without using sigma notation,...Ch. 12 - Prob. 9TCh. 12 - Prob. 11TCh. 12 - Prob. 12TCh. 12 - A puppy weighs 0.85 lb at birth, and each week he...Ch. 12 - Prob. 1PCh. 12 - Fitness Program Sheila decides to embark on a...Ch. 12 - Monthly Savings Program Alice opens a savings...Ch. 12 - Prob. 4PCh. 12 - Prob. 5PCh. 12 - Prob. 6PCh. 12 - Prob. 7PCh. 12 - Prob. 8PCh. 12 - Prob. 9P
Knowledge Booster
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Calculus: Early Transcendentals
    Calculus
    ISBN:9781285741550
    Author:James Stewart
    Publisher:Cengage Learning
    Thomas' Calculus (14th Edition)
    Calculus
    ISBN:9780134438986
    Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
    Publisher:PEARSON
    Calculus: Early Transcendentals (3rd Edition)
    Calculus
    ISBN:9780134763644
    Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
    Publisher:PEARSON
  • Calculus: Early Transcendentals
    Calculus
    ISBN:9781319050740
    Author:Jon Rogawski, Colin Adams, Robert Franzosa
    Publisher:W. H. Freeman
    Precalculus
    Calculus
    ISBN:9780135189405
    Author:Michael Sullivan
    Publisher:PEARSON
    Calculus: Early Transcendental Functions
    Calculus
    ISBN:9781337552516
    Author:Ron Larson, Bruce H. Edwards
    Publisher:Cengage Learning
  • Calculus: Early Transcendentals
    Calculus
    ISBN:9781285741550
    Author:James Stewart
    Publisher:Cengage Learning
    Thomas' Calculus (14th Edition)
    Calculus
    ISBN:9780134438986
    Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
    Publisher:PEARSON
    Calculus: Early Transcendentals (3rd Edition)
    Calculus
    ISBN:9780134763644
    Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
    Publisher:PEARSON
    Calculus: Early Transcendentals
    Calculus
    ISBN:9781319050740
    Author:Jon Rogawski, Colin Adams, Robert Franzosa
    Publisher:W. H. Freeman
    Precalculus
    Calculus
    ISBN:9780135189405
    Author:Michael Sullivan
    Publisher:PEARSON
    Calculus: Early Transcendental Functions
    Calculus
    ISBN:9781337552516
    Author:Ron Larson, Bruce H. Edwards
    Publisher:Cengage Learning
    Sequences and Series Introduction; Author: Mario's Math Tutoring;https://www.youtube.com/watch?v=m5Yn4BdpOV0;License: Standard YouTube License, CC-BY
    Introduction to sequences; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=VG9ft4_dK24;License: Standard YouTube License, CC-BY