a. Answer Explanation Calculation: Let us find the first 10 terms in the sequence The sequence is 3 + ( − 1 ) n The first 10 terms of the sequence given by 3 + ( − 1 ) n are a 1 = 3 + ( − 1 ) 1 a 1 = 2....... 1 st term a 2 = 3 + ( − 1 ) 2 a 2 = 4....... 2 nd term a 3 = 3 + ( − 1 ) 3 a 3 = 2....... 3 rd term a 4 = 3 + ( − 1 ) 4 a 4 = 4....... 4 th term a 5 = 3 + ( − 1 ) 5 a 5 = 2....... 5 th term a 6 = 3 + ( − 1 ) 6 a 6 = 4.......6 t h term a 7 = 3 + ( − 1 ) 7 a 7 = 2.......7 t h term a 8 = 3 + ( − 1 ) 8 a 8 = 4.......8 t h term a 9 = 3 + ( − 1 ) 9 a 9 = 2.......9 th term a 10 = 3 + ( − 1 ) 10 a 10 = 4.......10 th term Using the values derived above, we plot theses in the graph below b. To determine Describe the behaviour of the graph of the sequence. Answer odd a n = 2 , even a n = 4 Explanation Calculation: Hence, the graph in (a) shows that when n is odd a n = 2 and when n is even, a n = 4 c. To determine Complete the table. Answer n 1 10 101 1000 10 , 001 a n 2 4 2 4 2 Explanation Calculation: We put in different values of n in the given equation We have seen in (b) that when n is odd a n = 2 and when n is even, a n = 4 Using the above, we can fill the table as below Hence, we see that 1 , 101 , 10001 are odd and 10 and 1000 are even n 1 10 101 1000 10 , 001 a n 2 4 2 4 2 d. To determine Determine (if possible) the value of a n as n approaches infinity. Answer It is not possible to find the value of a n as n approaches infinity Explanation Calculation: We have seen in (b) that when n is odd a n = 2 and when n is even, a n = 4 This pattern continues as n approaches infinity Hence, it is not possible to find the value of a n , a s , n approaches infinity.

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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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

Chapter 9, Problem 2PS

To determine

Graph the first $10$ terms of the sequence.

Expert Solution

Answer to Problem 2PS

EBK PRECALCULUS W/LIMITS, Chapter 9, Problem 2PS , additional homework tip 1

Explanation of Solution

Calculation:

Let us find the first $10$ terms in the sequence

The sequence is $3+(−1)n$

The first $10$ terms of the sequence given by $3+(−1)n$ are

$a1=3+(−1)1a1=2.......1stterma2=3+(−1)2a2=4.......2ndterma3=3+(−1)3a3=2.......3rdterma4=3+(−1)4a4=4.......4thterma5=3+(−1)5a5=2.......5thterm$

$a6=3+(−1)6a6=4.......6thterma7=3+(−1)7a7=2.......7thterma8=3+(−1)8a8=4.......8thterma9=3+(−1)9a9=2.......9thterma10=3+(−1)10a10=4.......10thterm$

Using the values derived above, we plot theses in the graph below

EBK PRECALCULUS W/LIMITS, Chapter 9, Problem 2PS , additional homework tip 2

To determine

Describe the behaviour of the graph of the sequence.

Expert Solution

Answer to Problem 2PS

$odd an=2,even an=4$

Explanation of Solution

Calculation:

Hence, the graph in (a) shows that when $n$ is odd $an=2$ and when $n$ is even, $an=4$

To determine

Complete the table.

Expert Solution

Answer to Problem 2PS

$n110101100010,001an24242$

Explanation of Solution

Calculation:

We put in different values of $n$ in the given equation We have seen in (b) that when $n$ is odd $an=2$ and when $n$ is even, $an=4$

Using the above, we can fill the table as below

Hence, we see that $1,101,10001$ are odd and $10$ and $1000$ are even

$n110101100010,001an24242$

To determine

Determine (if possible) the value of $an$ as $n$ approaches infinity.

Expert Solution

Answer to Problem 2PS

It is not possible to find the value of $an$ as $n$ approaches infinity

Explanation of Solution

Calculation:

We have seen in (b) that when $n$ is odd $an=2$ and when $n$ is even, $an=4$

This pattern continues as $n$ approaches infinity

Hence, it is not possible to find the value of $an,as,n$ approaches infinity.

Chapter 9, Problem 1PS

Chapter 9, Problem 3PS

Chapter 9 Solutions

EBK PRECALCULUS W/LIMITS

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Prob. 47RE Ch. 9 - Prob. 48RE Ch. 9 - Prob. 49RE Ch. 9 - Prob. 50RE Ch. 9 - Prob. 51RE Ch. 9 - Prob. 52RE Ch. 9 - Prob. 53RE Ch. 9 - Prob. 54RE Ch. 9 - Prob. 55RE Ch. 9 - Prob. 56RE Ch. 9 - Prob. 57RE Ch. 9 - Prob. 58RE Ch. 9 - Prob. 59RE Ch. 9 - Prob. 60RE Ch. 9 - Prob. 61RE Ch. 9 - Prob. 62RE Ch. 9 - Prob. 63RE Ch. 9 - Prob. 64RE Ch. 9 - Prob. 65RE Ch. 9 - Prob. 66RE Ch. 9 - Prob. 67RE Ch. 9 - Prob. 68RE Ch. 9 - Prob. 69RE Ch. 9 - Prob. 70RE Ch. 9 - Prob. 71RE Ch. 9 - Prob. 72RE Ch. 9 - Prob. 73RE Ch. 9 - Prob. 74RE Ch. 9 - Prob. 75RE Ch. 9 - Prob. 76RE Ch. 9 - Prob. 77RE Ch. 9 - Prob. 78RE Ch. 9 - Prob. 79RE Ch. 9 - Prob. 80RE Ch. 9 - Prob. 81RE Ch. 9 - Prob. 82RE Ch. 9 - Prob. 83RE Ch. 9 - Prob. 84RE Ch. 9 - Prob. 85RE Ch. 9 - Prob. 86RE Ch. 9 - Prob. 87RE Ch. 9 - Prob. 88RE Ch. 9 - Prob. 89RE Ch. 9 - Prob. 90RE Ch. 9 - Prob. 91RE Ch. 9 - Prob. 92RE Ch. 9 - Prob. 93RE Ch. 9 - Prob. 94RE Ch. 9 - Prob. 95RE Ch. 9 - Prob. 96RE Ch. 9 - Prob. 97RE Ch. 9 - Prob. 98RE Ch. 9 - Prob. 99RE Ch. 9 - Prob. 100RE Ch. 9 - Prob. 101RE Ch. 9 - Prob. 102RE Ch. 9 - Prob. 103RE Ch. 9 - Prob. 104RE Ch. 9 - Prob. 105RE Ch. 9 - Prob. 106RE Ch. 9 - Prob. 107RE Ch. 9 - Prob. 108RE Ch. 9 - Prob. 1CT Ch. 9 - Prob. 2CT Ch. 9 - Prob. 3CT Ch. 9 - Prob. 4CT Ch. 9 - Prob. 5CT Ch. 9 - Prob. 6CT Ch. 9 - Prob. 7CT Ch. 9 - Prob. 8CT Ch. 9 - Prob. 9CT Ch. 9 - Prob. 10CT Ch. 9 - Prob. 11CT Ch. 9 - Prob. 12CT Ch. 9 - Prob. 13CT Ch. 9 - Prob. 14CT Ch. 9 - Prob. 15CT Ch. 9 - Prob. 16CT Ch. 9 - Prob. 17CT Ch. 9 - Prob. 18CT Ch. 9 - Prob. 19CT Ch. 9 - Prob. 20CT Ch. 9 - Prob. 1CLT Ch. 9 - Prob. 2CLT Ch. 9 - Prob. 3CLT Ch. 9 - Prob. 4CLT Ch. 9 - Prob. 5CLT Ch. 9 - Prob. 6CLT Ch. 9 - Prob. 7CLT Ch. 9 - Prob. 8CLT Ch. 9 - Prob. 9CLT Ch. 9 - Prob. 10CLT Ch. 9 - Prob. 11CLT Ch. 9 - Prob. 12CLT Ch. 9 - Prob. 13CLT Ch. 9 - Prob. 14CLT Ch. 9 - Prob. 15CLT Ch. 9 - Prob. 16CLT Ch. 9 - Prob. 17CLT Ch. 9 - Prob. 18CLT Ch. 9 - Prob. 19CLT Ch. 9 - Prob. 20CLT Ch. 9 - Prob. 21CLT Ch. 9 - Prob. 22CLT Ch. 9 - Prob. 23CLT Ch. 9 - Prob. 24CLT Ch. 9 - Prob. 25CLT Ch. 9 - Prob. 26CLT Ch. 9 - Prob. 27CLT Ch. 9 - Prob. 28CLT Ch. 9 - Prob. 29CLT Ch. 9 - Prob. 30CLT Ch. 9 - Prob. 31CLT Ch. 9 - Prob. 32CLT Ch. 9 - Prob. 33CLT Ch. 9 - Prob. 34CLT Ch. 9 - Prob. 35CLT Ch. 9 - Prob. 36CLT Ch. 9 - Prob. 37CLT Ch. 9 - Prob. 38CLT Ch. 9 - Prob. 39CLT Ch. 9 - Prob. 40CLT Ch. 9 - Prob. 41CLT Ch. 9 - Prob. 1PS Ch. 9 - Prob. 2PS Ch. 9 - Prob. 3PS Ch. 9 - Prob. 4PS Ch. 9 - Prob. 5PS Ch. 9 - Prob. 6PS Ch. 9 - Prob. 7PS Ch. 9 - Prob. 8PS Ch. 9 - Prob. 9PS Ch. 9 - Prob. 10PS Ch. 9 - Prob. 11PS Ch. 9 - Prob. 12PS Ch. 9 - Prob. 13PS Ch. 9 - Prob. 14PS Ch. 9 - Prob. 15PS Ch. 9 - Prob. 16PS

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