a. Answer n represents the number of blue pattern in each quilt and a n represents the blue squares. Explanation Given: The given pattern is Calculation: In the given pattern, n represents the number of blue pattern in each quilt and a n represents the blue squares. b. To determine Draw a table for the values of n and a n . Explanation Given: The given pattern is The given values of n = 1 , 2 , 3 , 4 , 5 , 6 , 7 , and 8 . Calculation: Find the values of a n for the given values of n = 1 , 2 , 3 , 4 , 5 , 6 , 7 , and 8 . From the pattern, 0 + 1 = 1 n = 1 , a n = 1 1 + 1 = 2 n = 2 , a n = 2 2 + 3 = 5 n = 3 , a n = 5 5 + 3 = 8 n = 4 , a n = 8 Similarly 8 + 5 = 13 n = 5 , a n = 13 13 + 5 = 18 n = 6 , a n = 18 18 + 7 = 25 n = 7 , a n = 25 25 + 7 = 32 n = 7 , a n = 32 Hence the table for the values of a n with respect to n is given below. n a n 1 2 3 4 5 6 7 8 1 2 5 8 13 18 25 32 c. To determine Find the values of a n for the values of n using given rule and compare with the result b . Answer The given rule represents the n th number of blue squares. Explanation Given: The given pattern is The given rule is a n = n 2 2 + 1 4 [ 1 − ( − 1 ) n ] and the values of n = 1 , 2 , 3 , 4 , 5 , 6 , 7 , and 8 . Calculation: Find the values of a n for the given values of n = 1 , 2 , 3 , 4 , 5 , 6 , 7 , and 8 . From the pattern, 0 + 1 = 1 n = 1 , a n = 1 1 + 1 = 2 n = 2 , a n = 2 2 + 3 = 5 n = 3 , a n = 5 5 + 3 = 8 n = 4 , a n = 8 Similarly 8 + 5 = 13 n = 5 , a n = 13 13 + 5 = 18 n = 6 , a n = 18 18 + 7 = 25 n = 7 , a n = 25 25 + 7 = 32 n = 7 , a n = 32 Hence the table for the values of a n with respect to n is given below. n a n 1 2 3 4 5 6 7 8 1 2 5 8 13 18 25 32 Find the values of a n using rule a n = n 2 2 + 1 4 [ 1 − ( − 1 ) n ] . n = 1 , a 1 = 1 2 2 + 1 4 [ 1 − ( − 1 ) 1 ] = 1 n = 2 , a 2 = 2 2 2 + 1 4 [ 1 − ( − 1 ) 2 ] = 2 n = 3 , a 3 = 3 2 2 + 1 4 [ 1 − ( − 1 ) 3 ] = 5 n = 4 , a 4 = 4 2 2 + 1 4 [ 1 − ( − 1 ) 4 ] = 8 n = 5 , a 5 = 5 2 2 + 1 4 [ 1 − ( − 1 ) 5 ] = 13 n = 6 , a 6 = 6 2 2 + 1 4 [ 1 − ( − 1 ) 6 ] = 18 n = 7 , a 7 = 7 2 2 + 1 4 [ 1 − ( − 1 ) 7 ] = 25 n = 8 , a 8 = 8 2 2 + 1 4 [ 1 − ( − 1 ) 8 ] = 32 From the above results, the results are same as the part b . Hence the given rule represents the n th number of blue squares.

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Chapter 8, Problem 13CT

To determine

Describe the meaning of $n$ and $an$ in the given pattern.

Expert Solution

Answer to Problem 13CT

$n$ represents the number of blue pattern in each quilt and $an$ represents the blue squares.

Explanation of Solution

Given:

The given pattern is

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 8, Problem 13CT , additional homework tip 1

Calculation:

In the given pattern, $n$ represents the number of blue pattern in each quilt and $an$ represents the blue squares.

To determine

Draw a table for the values of $n$ and $an$ .

Expert Solution

Explanation of Solution

Given:

The given pattern is

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 8, Problem 13CT , additional homework tip 2

The given values of $n=1,2,3,4,5,6,7, and 8$ .

Calculation:

Find the values of $an$ for the given values of $n=1,2,3,4,5,6,7, and 8$ .

From the pattern,

$0+1=1n=1,an=11+1=2n=2,an=22+3=5n=3,an=55+3=8n=4,an=8$

Similarly

$8+5=13n=5,an=1313+5=18n=6,an=1818+7=25n=7,an=2525+7=32n=7,an=32$

Hence the table for the values of $an$ with respect to $n$ is given below.

$n$	$an$
$12345678$	$125813182532$

To determine

Find the values of $an$ for the values of $n$ using given rule and compare with the result $b$ .

Expert Solution

Answer to Problem 13CT

The given rule represents the $nth$ number of blue squares.

Explanation of Solution

Given:

The given pattern is

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 8, Problem 13CT , additional homework tip 3

The given rule is $an=n22+14[1−(−1)n]$ and the values of $n=1,2,3,4,5,6,7, and 8$ .

Calculation:

Find the values of $an$ for the given values of $n=1,2,3,4,5,6,7, and 8$ .

From the pattern,

$0+1=1n=1,an=11+1=2n=2,an=22+3=5n=3,an=55+3=8n=4,an=8$

Similarly

$8+5=13n=5,an=1313+5=18n=6,an=1818+7=25n=7,an=2525+7=32n=7,an=32$

Hence the table for the values of $an$ with respect to $n$ is given below.

$n$	$an$
$12345678$	$125813182532$

Find the values of $an$ using rule $an=n22+14[1−(−1)n]$ .

$n=1,a1=122+14[1−(−1)1]=1n=2,a2=222+14[1−(−1)2]=2$

$n=3,a3=322+14[1−(−1)3]=5n=4,a4=422+14[1−(−1)4]=8$

$n=5,a5=522+14[1−(−1)5]=13n=6,a6=622+14[1−(−1)6]=18n=7,a7=722+14[1−(−1)7]=25n=8,a8=822+14[1−(−1)8]=32$

From the above results, the results are same as the part $b$ .

Hence the given rule represents the $nth$ number of blue squares.

Chapter 8, Problem 12CT

Chapter 8, Problem 14CT

Chapter 8 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.1 - Prob. 56E Ch. 8.1 - Prob. 57E Ch. 8.1 - Prob. 58E Ch. 8.1 - Prob. 59E Ch. 8.1 - Prob. 60E Ch. 8.1 - 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Describe the meaning of n and a n in the given pattern.

Concept explainers

Describe the meaning of n<m:math><m:mi>n</m:mi></m:math> and an<m:math><m:mrow><m:msub><m:mi>a</m:mi><m:mi>n</m:mi></m:msub></m:mrow></m:math> in the given pattern.

Answer to Problem 13CT

Explanation of Solution

Draw a table for the values of n<m:math><m:mi>n</m:mi></m:math> and an<m:math><m:mrow><m:msub><m:mi>a</m:mi><m:mi>n</m:mi></m:msub></m:mrow></m:math> .

Explanation of Solution

Find the values of an<m:math><m:mrow><m:msub><m:mi>a</m:mi><m:mi>n</m:mi></m:msub></m:mrow></m:math> for the values of n<m:math><m:mi>n</m:mi></m:math> using given rule and compare with the result b<m:math><m:mi>b</m:mi></m:math> .

Answer to Problem 13CT

Explanation of Solution

Chapter 8 Solutions

Describe the meaning of $n$ and $an$ in the given pattern.

Draw a table for the values of $n$ and $an$ .

Find the values of $an$ for the values of $n$ using given rule and compare with the result $b$ .