Excursions in Modern Mathematics (9th Edition)
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
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Chapter 9, Problem 1E

Consider the sequence defined by the explicit formula A N = N 2 + 1 .

a. Find A 1 .

b. Find A 100 .

c. Suppose A N = 10 . Find N.

Expert Solution
Check Mark
To determine

(a)

To find:

The specified value of A1 from the given sequence.

Answer to Problem 1E

Solution:

The value of A1 is 2.

Explanation of Solution

Given:

The sequence with an explicit formula AN=N2+1.

Calculation:

The given sequence is AN=N2+1.

To obtain A1 substitute 1 for N in the above formula.

A1=12+1=2

Therefore, the value of A1 is 2.

Conclusion:

The value of A1 is 2.

Expert Solution
Check Mark
To determine

(b)

To find:

The specified value of A100 from the given sequence.

Answer to Problem 1E

Solution:

The value of A100 is 10001.

Explanation of Solution

Given:

The sequence with an explicit formula AN=N2+1.

Calculation:

The given sequence is AN=N2+1.

To obtain A100 substitute 100 for N in the above formula.

A100=1002+1=10001

Therefore, the value of A100 is 10001.

Conclusion:

The value of A100 is 10001.

Expert Solution
Check Mark
To determine

(c)

To find:

The value of N for the given value of AN.

Answer to Problem 1E

Solution:

The value of N is 3.

Explanation of Solution

Given:

The sequence with an explicit formula AN=N2+1.

The given value of AN is 10.

Calculation:

The given sequence is AN=N2+1.

Substitute 10 for AN in the above formula.

10=N2+1N2=101N=9=3

Therefore, the value of N is 3.

Conclusion:

The value of N is 3.

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Chapter 9 Solutions

Excursions in Modern Mathematics (9th Edition)

Ch. 9 - Consider the sequence 1,2,6,24,120,.... a. List...Ch. 9 - Consider the sequence 0,1,3,6,10,15,21.... a. List...Ch. 9 - Prob. 14ECh. 9 - Consider the sequence 1,85,2,167,208,.... a. List...Ch. 9 - Prob. 16ECh. 9 - Airlines would like to board passengers in the...Ch. 9 - When two fair coins are tossed the probability of...Ch. 9 - Consider a population that grows linearly...Ch. 9 - Consider a population that grows linearly...Ch. 9 - Consider a population that grows linearly...Ch. 9 - Consider a population that grows linearly...Ch. 9 - Consider a population that grows linearly, with...Ch. 9 - Consider a population that grows linearly, with...Ch. 9 - Official unemployment rates for the U.S....Ch. 9 - The world population reached 6 billion people in...Ch. 9 - The Social Security Administration uses a linear...Ch. 9 - While the number of smokers for the general adult...Ch. 9 - Use the arithmetic sum formula to find the sum...Ch. 9 - Prob. 30ECh. 9 - An arithmetic sequence has first term P0=12 and...Ch. 9 - An arithmetic sequence has first term P0=1 and...Ch. 9 - Find the sum a. 1+3+5+7++149.Hint: See Example...Ch. 9 - Find the sum a. 2+4+6++98. b. 2+4+6+75terms.Ch. 9 - The city of Lightsville currently has 137...Ch. 9 - Prob. 36ECh. 9 - A population grows according to an exponential...Ch. 9 - A population grows according to an exponential...Ch. 9 - A population grows according to the recursive rule...Ch. 9 - Prob. 40ECh. 9 - Crime in Happyville is on the rise. Each year the...Ch. 9 - Prob. 42ECh. 9 - Prob. 43ECh. 9 - Avian influenza A H5N1 is a particularly virulent...Ch. 9 - In 2010 the undergraduate enrollment at Bright...Ch. 9 - In 2009 there were 73 cases of avian influenza A...Ch. 9 - Consider the geometric sequence P0=2, P1=6, P2=18,...Ch. 9 - Consider the geometric sequence P0=4, P1=6, P2=9,...Ch. 9 - Consider the geometric sequence P0=4, P1=2, P2=1,....Ch. 9 - Consider the geometric sequence P0=10, P1=2,...Ch. 9 - Find the sum a. 1+2+22+23++215. b. 1+2+22+23++2N1...Ch. 9 - Find the sum a. 1+3+32+33++310. b. 1+3+32+33++3N1....Ch. 9 - A population grows according to the logistic...Ch. 9 - A population grows according to the logistic...Ch. 9 - For the population discussed in Exercise 53...Ch. 9 - Prob. 56ECh. 9 - Prob. 57ECh. 9 - Prob. 58ECh. 9 - Prob. 59ECh. 9 - Prob. 60ECh. 9 - A population grows according to the logistic...Ch. 9 - A population grows according to the logistic...Ch. 9 - Each of the following sequences follows a linear,...Ch. 9 - Each of the line graph shown in Figs. 9-19 through...Ch. 9 - Prob. 65ECh. 9 - Prob. 66ECh. 9 - Prob. 67ECh. 9 - Prob. 68ECh. 9 - Prob. 69ECh. 9 - Prob. 70ECh. 9 - Prob. 71ECh. 9 - Prob. 72ECh. 9 - Prob. 73ECh. 9 - Prob. 74ECh. 9 - Prob. 75ECh. 9 - Show that if P0,P1,P2,... is an arithmetic...

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