Algebra and Trigonometry
Algebra and Trigonometry
4th Edition
ISBN: 9781305719781
Author: James Stewart, Lothar Redlin, Saleem Watson
Publisher: PEARSON
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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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Chapter 13.2, Problem 31E

27-32 ■ Arithmetic Sequence? Find the first five terms of the sequence, and determine whether it is arithmetic. If it is arithmetic, find the common difference, and express the nth term of the sequence in the standard form a n = a + ( n − 1 ) d .

a n = 6 n − 10

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Chapter 13 Solutions

Algebra and Trigonometry

Ch. 13.1 - CONCEPTS A sequence is a function whose domain is...Ch. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - 3-14, Terms of a Sequence Find the first four...Ch. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10E
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - 3-14 Terms of a Sequence Find the first four...Ch. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - 15-20 Recursive Sequence A sequence is defined...Ch. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Prob. 23ECh. 13.1 - Prob. 24ECh. 13.1 - SKILLS 21-26 Terms of a Sequence Use a graphing...Ch. 13.1 - Prob. 26ECh. 13.1 - 27-38 nth term of a Sequence Find the nth term of...Ch. 13.1 - Prob. 28ECh. 13.1 - Prob. 29ECh. 13.1 - Prob. 30ECh. 13.1 - SKILLS 27-38 nth term of a Sequence Find the nth...Ch. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - SKILLS 27-38 nth term of a Sequence Find the nth...Ch. 13.1 - SKILLS 27-38 nth term of a Sequence Find the nth...Ch. 13.1 - Prob. 38ECh. 13.1 - Prob. 39ECh. 13.1 - Prob. 40ECh. 13.1 - Prob. 41ECh. 13.1 - Prob. 42ECh. 13.1 - SKILLS 43-46 nth Partial Sums Find the first four...Ch. 13.1 - Prob. 44ECh. 13.1 - Prob. 45ECh. 13.1 - Prob. 46ECh. 13.1 - Prob. 47ECh. 13.1 - Prob. 48ECh. 13.1 - 47-54 Evaluating a sum Find the sum. k=131kCh. 13.1 - 47-54 Evaluating a sum Find the sum. j=1100(1)jCh. 13.1 - Prob. 51ECh. 13.1 - Prob. 52ECh. 13.1 - Prob. 53ECh. 13.1 - 47-54 Evaluating a sum Find the sum. i=13i2iCh. 13.1 - 55-60 Evaluating a SumUse a graphing calculator to...Ch. 13.1 - Prob. 56ECh. 13.1 - Prob. 57ECh. 13.1 - Prob. 58ECh. 13.1 - Prob. 59ECh. 13.1 - Prob. 60ECh. 13.1 - 61-66 Sigma Notation Write the sum without using...Ch. 13.1 - Prob. 62ECh. 13.1 - Prob. 63ECh. 13.1 - Prob. 64ECh. 13.1 - Prob. 65ECh. 13.1 - Prob. 66ECh. 13.1 - 67-74 Sigma Notation Write the sum using sigma...Ch. 13.1 - Prob. 68ECh. 13.1 - Prob. 69ECh. 13.1 - 67-74 Sigma Notation Write the sum using sigma...Ch. 13.1 - Prob. 71ECh. 13.1 - Prob. 72ECh. 13.1 - 67-74 Sigma Notation Write the sum using sigma...Ch. 13.1 - Prob. 74ECh. 13.1 - Prob. 75ECh. 13.1 - Prob. 76ECh. 13.1 - Prob. 77ECh. 13.1 - Prob. 78ECh. 13.1 - Prob. 79ECh. 13.1 - Prob. 80ECh. 13.1 - Prob. 81ECh. 13.1 - Prob. 82ECh. 13.1 - Prob. 83ECh. 13.1 - Prob. 84ECh. 13.1 - Fibonaccis RabbitsFibonacci posed the following...Ch. 13.1 - Prob. 86ECh. 13.1 - Prob. 87ECh. 13.1 - Prob. 88ECh. 13.2 - An arithmetic sequence is a sequence in which the...Ch. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - 5-10Terms of an Arithmetic SequenceThe nth term of...Ch. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - 11-16 nth term of an Arithmetic Sequence Find the...Ch. 13.2 - Prob. 12ECh. 13.2 - 11-16 nth term of an Arithmetic Sequence Find the...Ch. 13.2 - 11-16 nth term of an Arithmetic Sequence Find the...Ch. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - 17-26 Arithmetic Sequence? The first four terms...Ch. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - 17-26 Arithmetic Sequence? The first four terms...Ch. 13.2 - 17-26 Arithmetic Sequence? The first four terms...Ch. 13.2 - Prob. 26ECh. 13.2 - Prob. 27ECh. 13.2 - Prob. 28ECh. 13.2 - Prob. 29ECh. 13.2 - Prob. 30ECh. 13.2 - 27-32 Arithmetic Sequence? Find the first five...Ch. 13.2 - Prob. 32ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - 33-44 Terms of an Arithmetic sequence Determine...Ch. 13.2 - Prob. 38ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.2 - Prob. 41ECh. 13.2 - Prob. 42ECh. 13.2 - 33-44 Terms of an Arithmetic sequence Determine...Ch. 13.2 - Prob. 44ECh. 13.2 - Prob. 45ECh. 13.2 - Prob. 46ECh. 13.2 - Prob. 47ECh. 13.2 - Prob. 48ECh. 13.2 - 45-50 Finding Terms of an Arithmetic sequence Find...Ch. 13.2 - Prob. 50ECh. 13.2 - Prob. 51ECh. 13.2 - Prob. 52ECh. 13.2 - Prob. 53ECh. 13.2 - 51-56 Partial Sum of an Arithmetic Sequence Find...Ch. 13.2 - 51-56 Partial Sum of an Arithmetic Sequence Find...Ch. 13.2 - Prob. 56ECh. 13.2 - Prob. 57ECh. 13.2 - Prob. 58ECh. 13.2 - Prob. 59ECh. 13.2 - 57-64 Partial Sums of an Arithmetic Sequence A...Ch. 13.2 - 57-64 Partial Sums of an Arithmetic Sequence A...Ch. 13.2 - Prob. 62ECh. 13.2 - Prob. 63ECh. 13.2 - Prob. 64ECh. 13.2 - Prob. 65ECh. 13.2 - Prob. 66ECh. 13.2 - Special Triangle Show that a right triangle whose...Ch. 13.2 - Prob. 68ECh. 13.2 - Prob. 69ECh. 13.2 - Harmonic Mean The harmonic mean of two numbers is...Ch. 13.2 - Prob. 71ECh. 13.2 - Poles in a Pile Telephone poles are being stored...Ch. 13.2 - Salary IncreasesA man gets a job with a salary of...Ch. 13.2 - Prob. 74ECh. 13.2 - Theater Seating An architect designs a theater...Ch. 13.2 - Prob. 76ECh. 13.2 - Prob. 77ECh. 13.2 - Prob. 78ECh. 13.3 - CONCEPTS A geometric sequence is a sequence in...Ch. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - SKILLS 58nthTerm of a Geometric Sequence The nth...Ch. 13.3 - Prob. 6ECh. 13.3 - SKILLS 58nthTerm of a Geometric Sequence The nth...Ch. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - SKILLS 13-22Geometric Sequence?The first four...Ch. 13.3 - Prob. 14ECh. 13.3 - Prob. 15ECh. 13.3 - Prob. 16ECh. 13.3 - Prob. 17ECh. 13.3 - Prob. 18ECh. 13.3 - SKILLS 13-22 Geometric Sequence? The first four...Ch. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Prob. 24ECh. 13.3 - 23-28. Geometric Sequence?Find the first five...Ch. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 29ECh. 13.3 - Prob. 30ECh. 13.3 - 29-38 Terms of a geometric sequenceDetermine the...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - Prob. 34ECh. 13.3 - Prob. 35ECh. 13.3 - Prob. 36ECh. 13.3 - 2938Terms of a Geometric SequenceDetermine the...Ch. 13.3 - Prob. 38ECh. 13.3 - Prob. 39ECh. 13.3 - 3946 Finding Terms of a Geometric Sequence Find...Ch. 13.3 - The third term is 13 and the sixth term is 9. Find...Ch. 13.3 - The fourth term is 12 and the seventh term is...Ch. 13.3 - The third term is 18 and the sixth term is 9216....Ch. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - 49-52 Partial Sums of a Geometric Sequence Find...Ch. 13.3 - Prob. 50ECh. 13.3 - Prob. 51ECh. 13.3 - Prob. 52ECh. 13.3 - Prob. 53ECh. 13.3 - 53-58 Partial Sums of a Geometric Sequence Find...Ch. 13.3 - 53-58 Partial Sums of a Geometric Sequence Find...Ch. 13.3 - Prob. 56ECh. 13.3 - Prob. 57ECh. 13.3 - Prob. 58ECh. 13.3 - Prob. 59ECh. 13.3 - Prob. 60ECh. 13.3 - SKILLS 59-64 Partial Sums of a Geometric Sequence...Ch. 13.3 - Prob. 62ECh. 13.3 - Prob. 63ECh. 13.3 - Prob. 64ECh. 13.3 - Prob. 65ECh. 13.3 - Prob. 66ECh. 13.3 - SKILLS 65-76 Infinite Geometric Sequence...Ch. 13.3 - Prob. 68ECh. 13.3 - Prob. 69ECh. 13.3 - Prob. 70ECh. 13.3 - Prob. 71ECh. 13.3 - Prob. 72ECh. 13.3 - SKILLS 65-76 Infinite Geometric Sequence...Ch. 13.3 - Prob. 74ECh. 13.3 - Prob. 75ECh. 13.3 - Prob. 76ECh. 13.3 - Prob. 77ECh. 13.3 - Prob. 78ECh. 13.3 - Prob. 79ECh. 13.3 - Prob. 80ECh. 13.3 - Prob. 81ECh. 13.3 - Prob. 82ECh. 13.3 - Prob. 83ECh. 13.3 - Prob. 84ECh. 13.3 - Prob. 85ECh. 13.3 - Prob. 86ECh. 13.3 - Prob. 87ECh. 13.3 - Prob. 88ECh. 13.3 - Prob. 89ECh. 13.3 - Prob. 90ECh. 13.3 - Prob. 91ECh. 13.3 - Musical FrequenciesThe frequencies of musical...Ch. 13.3 - Prob. 93ECh. 13.3 - Geometric Savings Plan A very patient women wishes...Ch. 13.3 - St. Ives The following is a well-known childrens...Ch. 13.3 - Prob. 96ECh. 13.3 - Prob. 97ECh. 13.3 - Prob. 98ECh. 13.3 - Geometry The midpoints of the sides of a square of...Ch. 13.3 - Geometry A circular disk of radius R is cut out of...Ch. 13.3 - Geometry A yellow square of side 1 is divided into...Ch. 13.3 - Prob. 102ECh. 13.3 - Prob. 103ECh. 13.3 - Prob. 104ECh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13.4 - Prob. 8ECh. 13.4 - Prob. 9ECh. 13.4 - Prob. 10ECh. 13.4 - Prob. 11ECh. 13.4 - Prob. 12ECh. 13.4 - Prob. 13ECh. 13.4 - Prob. 14ECh. 13.4 - Prob. 15ECh. 13.4 - Prob. 16ECh. 13.4 - Prob. 17ECh. 13.4 - Prob. 18ECh. 13.4 - APPLICATIONS MortgageDr. Gupta is considering a...Ch. 13.4 - APPLICATIONS MortgageA couple can afford to make a...Ch. 13.4 - Prob. 21ECh. 13.4 - Prob. 22ECh. 13.4 - Prob. 23ECh. 13.4 - Prob. 24ECh. 13.4 - Prob. 25ECh. 13.4 - Prob. 26ECh. 13.4 - Interest Rate An item at a department store is...Ch. 13.4 - Prob. 28ECh. 13.4 - Prob. 29ECh. 13.4 - Prob. 30ECh. 13.4 - Prob. 31ECh. 13.5 - Prob. 1ECh. 13.5 - Prob. 2ECh. 13.5 - Prob. 3ECh. 13.5 - Prob. 4ECh. 13.5 - Prob. 5ECh. 13.5 - Prob. 6ECh. 13.5 - Prob. 7ECh. 13.5 - Prob. 8ECh. 13.5 - Prob. 9ECh. 13.5 - Prob. 10ECh. 13.5 - Prob. 11ECh. 13.5 - Prob. 12ECh. 13.5 - Prob. 13ECh. 13.5 - Prob. 14ECh. 13.5 - Prob. 15ECh. 13.5 - Prob. 16ECh. 13.5 - Prob. 17ECh. 13.5 - Prob. 18ECh. 13.5 - Prob. 19ECh. 13.5 - Prob. 20ECh. 13.5 - Prob. 21ECh. 13.5 - Prob. 22ECh. 13.5 - Prob. 23ECh. 13.5 - Prob. 24ECh. 13.5 - Prob. 25ECh. 13.5 - Prob. 26ECh. 13.5 - Prob. 27ECh. 13.5 - Prob. 28ECh. 13.5 - Prob. 29ECh. 13.5 - Prob. 30ECh. 13.5 - Prob. 31ECh. 13.5 - Prob. 32ECh. 13.5 - Prob. 33ECh. 13.5 - Prob. 34ECh. 13.5 - Prob. 35ECh. 13.5 - Prob. 36ECh. 13.5 - Prob. 37ECh. 13.5 - Prob. 38ECh. 13.6 - Prob. 1ECh. 13.6 - Prob. 2ECh. 13.6 - Prob. 3ECh. 13.6 - Prob. 4ECh. 13.6 - Prob. 5ECh. 13.6 - Prob. 6ECh. 13.6 - Prob. 7ECh. 13.6 - Prob. 8ECh. 13.6 - Prob. 9ECh. 13.6 - Prob. 10ECh. 13.6 - Prob. 11ECh. 13.6 - Prob. 12ECh. 13.6 - Prob. 13ECh. 13.6 - Prob. 14ECh. 13.6 - Prob. 15ECh. 13.6 - Prob. 16ECh. 13.6 - Prob. 17ECh. 13.6 - Prob. 18ECh. 13.6 - Prob. 19ECh. 13.6 - Prob. 20ECh. 13.6 - Prob. 21ECh. 13.6 - Prob. 22ECh. 13.6 - Prob. 23ECh. 13.6 - Prob. 24ECh. 13.6 - Prob. 25ECh. 13.6 - Prob. 26ECh. 13.6 - Prob. 27ECh. 13.6 - Prob. 28ECh. 13.6 - Prob. 29ECh. 13.6 - Prob. 30ECh. 13.6 - Prob. 31ECh. 13.6 - Prob. 32ECh. 13.6 - Prob. 33ECh. 13.6 - Prob. 34ECh. 13.6 - Prob. 35ECh. 13.6 - Prob. 36ECh. 13.6 - Prob. 37ECh. 13.6 - Prob. 38ECh. 13.6 - Prob. 39ECh. 13.6 - Prob. 40ECh. 13.6 - Prob. 41ECh. 13.6 - 29-42 Terms of a Binomial Expansion Find the...Ch. 13.6 - Prob. 43ECh. 13.6 - Prob. 44ECh. 13.6 - Prob. 45ECh. 13.6 - Prob. 46ECh. 13.6 - Prob. 47ECh. 13.6 - Prob. 48ECh. 13.6 - Prob. 49ECh. 13.6 - Prob. 50ECh. 13.6 - Prob. 51ECh. 13.6 - Prob. 52ECh. 13.6 - Prob. 53ECh. 13.6 - Prob. 54ECh. 13.6 - Prob. 55ECh. 13.6 - Prob. 56ECh. 13.6 - Prob. 57ECh. 13.6 - Prob. 58ECh. 13.6 - Prob. 59ECh. 13.CR - Prob. 1CCCh. 13.CR - Prob. 2CCCh. 13.CR - Prob. 3CCCh. 13.CR - Prob. 4CCCh. 13.CR - Prob. 5CCCh. 13.CR - Prob. 6CCCh. 13.CR - Prob. 7CCCh. 13.CR - Prob. 8CCCh. 13.CR - Prob. 9CCCh. 13.CR - Prob. 10CCCh. 13.CR - Prob. 11CCCh. 13.CR - Prob. 12CCCh. 13.CR - Prob. 1ECh. 13.CR - 1-6 Terms of a Sequence Find the first four terms...Ch. 13.CR - Prob. 3ECh. 13.CR - Prob. 4ECh. 13.CR - Prob. 5ECh. 13.CR - Prob. 6ECh. 13.CR - Prob. 7ECh. 13.CR - Prob. 8ECh. 13.CR - Prob. 9ECh. 13.CR - Prob. 10ECh. 13.CR - Prob. 11ECh. 13.CR - Prob. 12ECh. 13.CR - Prob. 13ECh. 13.CR - Prob. 14ECh. 13.CR - Prob. 15ECh. 13.CR - Prob. 16ECh. 13.CR - Prob. 17ECh. 13.CR - Prob. 18ECh. 13.CR - Prob. 19ECh. 13.CR - Prob. 20ECh. 13.CR - Prob. 21ECh. 13.CR - Prob. 22ECh. 13.CR - Prob. 23ECh. 13.CR - Prob. 24ECh. 13.CR - Prob. 25ECh. 13.CR - Prob. 26ECh. 13.CR - Prob. 27ECh. 13.CR - Prob. 28ECh. 13.CR - Prob. 29ECh. 13.CR - Prob. 30ECh. 13.CR - Bacteria Culture A certain type of bacteria...Ch. 13.CR - Prob. 32ECh. 13.CR - Prob. 33ECh. 13.CR - Arithmetic or Geometric? a If a1,a2,a3,... is an...Ch. 13.CR - Prob. 35ECh. 13.CR - Arithmetic and Geometric Sequences Find the values...Ch. 13.CR - Prob. 37ECh. 13.CR - Prob. 38ECh. 13.CR - Prob. 39ECh. 13.CR - Prob. 40ECh. 13.CR - Prob. 41ECh. 13.CR - Prob. 42ECh. 13.CR - Prob. 43ECh. 13.CR - Prob. 44ECh. 13.CR - Prob. 45ECh. 13.CR - Prob. 46ECh. 13.CR - Prob. 47ECh. 13.CR - Prob. 48ECh. 13.CR - Prob. 49ECh. 13.CR - Prob. 50ECh. 13.CR - Prob. 51ECh. 13.CR - Prob. 52ECh. 13.CR - Prob. 53ECh. 13.CR - Prob. 54ECh. 13.CR - Prob. 55ECh. 13.CR - Prob. 56ECh. 13.CR - Prob. 57ECh. 13.CR - Prob. 58ECh. 13.CR - Prob. 59ECh. 13.CR - Prob. 60ECh. 13.CR - Prob. 61ECh. 13.CR - Prob. 62ECh. 13.CR - Prob. 63ECh. 13.CR - Prob. 64ECh. 13.CR - Prob. 65ECh. 13.CR - Prob. 66ECh. 13.CR - Prob. 67ECh. 13.CR - Prob. 68ECh. 13.CR - Prob. 69ECh. 13.CR - Prob. 70ECh. 13.CR - Prob. 71ECh. 13.CR - Prob. 72ECh. 13.CR - Prob. 73ECh. 13.CR - Prob. 74ECh. 13.CR - Prob. 75ECh. 13.CR - Prob. 76ECh. 13.CR - Prob. 77ECh. 13.CR - Prob. 78ECh. 13.CR - Prob. 79ECh. 13.CR - Prob. 80ECh. 13.CR - Prob. 81ECh. 13.CR - Prob. 82ECh. 13.CR - Prob. 83ECh. 13.CT - Prob. 1CTCh. 13.CT - Prob. 2CTCh. 13.CT - Prob. 3CTCh. 13.CT - Prob. 4CTCh. 13.CT - The first term of a geometric sequence is 25, and...Ch. 13.CT - Prob. 6CTCh. 13.CT - Prob. 7CTCh. 13.CT - Prob. 8CTCh. 13.CT - Prob. 9CTCh. 13.CT - Prob. 10CTCh. 13.CT - Prob. 11CTCh. 13.CT - Prob. 12CTCh. 13.CT - Prob. 13CTCh. 13.FOM - Retirement Accounts Many college professors keep...Ch. 13.FOM - Prob. 2PCh. 13.FOM - Monthly Savings Program Alice opens a savings...Ch. 13.FOM - Pollution A chemical plant discharges 2400tons of...Ch. 13.FOM - Prob. 5PCh. 13.FOM - Prob. 6P
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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