McDougal Littell Jurgensen Geometry: Student Edition Geometry
McDougal Littell Jurgensen Geometry: Student Edition Geometry
5th Edition
ISBN: 9780395977279
Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Publisher: Houghton Mifflin Company College Division
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Chapter 3.6, Problem 28WE

a.

To determine

To calculate: the value for the given expression by substituting n = 1 to 9 .

a.

Expert Solution
Check Mark

Answer to Problem 28WE

  n2+n+11 = 13, 17, 23, 31, 41, 53, 67, 83, 101 for n = 1 to 9

Explanation of Solution

Given information: n2+n+11

Calculation :

For n=1 , n2+n+11=12+1+11=13

  n=2 , n2+n+11=22+2+11=17

  n=3 , n2+n+11=32+3+11=23

  n=4 , n2+n+11=42+4+11=31

  n=5 , n2+n+11=52+5+11=41

  n=6 , n2+n+11=62+6+11=53

  n=7 , n2+n+11=72+7+11=67

  n=8 , n2+n+11=82+8+11=83

  n=9 , n2+n+11=92+9+11=101

b.

To determine

To identify: using inductive reasoning a suitable guess for the value of n2+n+11 , for any positive value for n.

b.

Expert Solution
Check Mark

Answer to Problem 28WE

  f(n)=f(n1)+2n

Explanation of Solution

Given information: n2+n+11

From Sub-part (a):

    n 1 2 3 4 5 6 7 8 9

      n2+n+11

    13 17 23 31 41 53 67 83 101

  McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.6, Problem 28WE

From the above relationship, it can be guessed that the value for f(n)=n2+n+11 can be given as:

  f(n)=f(n1)+2n , for n2

c.

To determine

To verify: whether the guess for the given expression is correct by substituting n = 10, 11

c.

Expert Solution
Check Mark

Explanation of Solution

Given information: n2+n+11

Verification:

For

  n=10 , n2+n+11=100+10+11=121

  n=11 , n2+n+11=121+11+11=143

Using the guess: f(n)=f(n1)+2n for n2

For

  n=10 , f(10)=f(9)+(2×10)=101+20=121

  n=11

, f(11)=f(10)+(2×11)=121+22=143

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 3.1 - Prob. 11CECh. 3.1 - Prob. 12CECh. 3.1 - Prob. 13CECh. 3.1 - Prob. 14CECh. 3.1 - Prob. 15CECh. 3.1 - Prob. 16CECh. 3.1 - Prob. 17CECh. 3.1 - Prob. 18CECh. 3.1 - Prob. 19CECh. 3.1 - Prob. 1WECh. 3.1 - Prob. 2WECh. 3.1 - Prob. 3WECh. 3.1 - Prob. 4WECh. 3.1 - Prob. 5WECh. 3.1 - Prob. 6WECh. 3.1 - Prob. 7WECh. 3.1 - Prob. 8WECh. 3.1 - Prob. 9WECh. 3.1 - Prob. 10WECh. 3.1 - Prob. 11WECh. 3.1 - Prob. 12WECh. 3.1 - Prob. 13WECh. 3.1 - Prob. 14WECh. 3.1 - Prob. 15WECh. 3.1 - Prob. 16WECh. 3.1 - Prob. 17WECh. 3.1 - Prob. 18WECh. 3.1 - Prob. 19WECh. 3.1 - Prob. 20WECh. 3.1 - Prob. 21WECh. 3.1 - Prob. 22WECh. 3.1 - Prob. 23WECh. 3.1 - Prob. 24WECh. 3.1 - Prob. 25WECh. 3.1 - Prob. 26WECh. 3.1 - Prob. 27WECh. 3.1 - Prob. 28WECh. 3.1 - Prob. 29WECh. 3.1 - Prob. 30WECh. 3.1 - Prob. 31WECh. 3.1 - Prob. 32WECh. 3.1 - Prob. 33WECh. 3.1 - Prob. 34WECh. 3.1 - Prob. 35WECh. 3.1 - Prob. 36WECh. 3.1 - Prob. 37WECh. 3.1 - Prob. 38WECh. 3.1 - Prob. 39WECh. 3.1 - Prob. 40WECh. 3.1 - Prob. 41WECh. 3.1 - 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Prob. 28WECh. 3.6 - Prob. 1CECh. 3.6 - Prob. 2CECh. 3.6 - Prob. 3CECh. 3.6 - Prob. 4CECh. 3.6 - Prob. 5CECh. 3.6 - Prob. 6CECh. 3.6 - Prob. 1WECh. 3.6 - Prob. 2WECh. 3.6 - Prob. 3WECh. 3.6 - Prob. 4WECh. 3.6 - Prob. 5WECh. 3.6 - Prob. 6WECh. 3.6 - Prob. 7WECh. 3.6 - Prob. 8WECh. 3.6 - Prob. 9WECh. 3.6 - Prob. 10WECh. 3.6 - Prob. 11WECh. 3.6 - Prob. 12WECh. 3.6 - Prob. 13WECh. 3.6 - Prob. 14WECh. 3.6 - Prob. 15WECh. 3.6 - Prob. 16WECh. 3.6 - Prob. 17WECh. 3.6 - Prob. 18WECh. 3.6 - Prob. 19WECh. 3.6 - Prob. 20WECh. 3.6 - Prob. 21WECh. 3.6 - Prob. 22WECh. 3.6 - Prob. 23WECh. 3.6 - Prob. 24WECh. 3.6 - Prob. 25WECh. 3.6 - Prob. 26WECh. 3.6 - Prob. 27WECh. 3.6 - Prob. 28WECh. 3.6 - Prob. 29WECh. 3.6 - Prob. 30WECh. 3.6 - Prob. 1ST2Ch. 3.6 - Prob. 2ST2Ch. 3.6 - Prob. 3ST2Ch. 3.6 - Prob. 4ST2Ch. 3.6 - Prob. 5ST2Ch. 3.6 - Prob. 6ST2Ch. 3.6 - Prob. 7ST2Ch. 3.6 - Prob. 8ST2Ch. 3.6 - Prob. 9ST2Ch. 3.6 - Prob. 10ST2Ch. 3.6 - Prob. 11ST2Ch. 3.6 - Prob. 12ST2Ch. 3.6 - Prob. 13ST2Ch. 3.6 - Prob. 14ST2Ch. 3.6 - 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