Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 11.5, Problem 46PPS

(a)

To determine

Write a sequence of the total number of triangles in the first six figures.

(a)

Expert Solution
Check Mark

Answer to Problem 46PPS

The sequence is 1,4,10,19,31,46

Explanation of Solution

Given:

  Algebra 2, Chapter 11.5, Problem 46PPS , additional homework tip  1

Write a sequence of the total number of triangles in the first six figures.

Concept Used:

The number of Triangles in First figure is 1 and in second figure is 4 and in third figure is 10.

Calculation:

  a1=1,a2=4,a3=104=1+3(21)10=4+3(31)an=an1+3(n1)

  Therefore:a4=a3+3(n1)=10+3(41)=19a5=a4+3(n1)=19+3(51)=31a6=a5+3(n1)=31+3(61)=46

Thus, the sequence is 1,4,10,19,31,46

(b)

To determine

Write a recursive formula for the number of triangles.

(b)

Expert Solution
Check Mark

Answer to Problem 46PPS

The recursive formula is an=an1+3(n1)

Explanation of Solution

Given:

  Algebra 2, Chapter 11.5, Problem 46PPS , additional homework tip  2

Write a recursive formula for the number of triangles.

Concept Used:

The number of Triangles in First figure is 1 and in second figure is 4 and in third figure is 10.

Calculation:

The sequence is 1,4,10,19,31,46

The recursive formula is an=an1+3(n1)

Thus, the recursive formula is an=an1+3(n1)

(c)

To determine

Find the number of triangles in the tenth figure.

(c)

Expert Solution
Check Mark

Answer to Problem 46PPS

The number of triangles in the tenth figure is 136

Explanation of Solution

Given:

  Algebra 2, Chapter 11.5, Problem 46PPS , additional homework tip  3

How many triangles will be in the tenth figure?

Concept Used:

The number of Triangles in First figure is 1 and in second figure is 4 and in third figure is 10.

Calculation:

The recursive formula is an=an1+3(n1)

  a7=a6+3(n1)=46+3(71)=64a8=a7+3(n1)=31+3(81)=85a9=a8+3(n1)=31+3(91)=109a10=a9+3(n1)=31+3(101)=136

The number of triangles in the tenth figure is 136

Thus, the number of triangles in the tenth figure is 136

Chapter 11 Solutions

Algebra 2

Ch. 11.1 - Prob. 1CYUCh. 11.1 - Prob. 2CYUCh. 11.1 - Prob. 3CYUCh. 11.1 - Prob. 4CYUCh. 11.1 - Prob. 5CYUCh. 11.1 - Prob. 6CYUCh. 11.1 - Prob. 7CYUCh. 11.1 - Prob. 8CYUCh. 11.1 - Prob. 9CYUCh. 11.1 - Prob. 10CYUCh. 11.1 - Prob. 11CYUCh. 11.1 - Prob. 12CYUCh. 11.1 - Prob. 13CYUCh. 11.1 - Prob. 14CYUCh. 11.1 - Prob. 15CYUCh. 11.1 - Prob. 16CYUCh. 11.1 - Prob. 17CYUCh. 11.1 - Prob. 18CYUCh. 11.1 - Prob. 19CYUCh. 11.1 - Prob. 20CYUCh. 11.1 - Prob. 21PPSCh. 11.1 - Prob. 22PPSCh. 11.1 - Prob. 23PPSCh. 11.1 - Prob. 24PPSCh. 11.1 - Prob. 25PPSCh. 11.1 - Prob. 26PPSCh. 11.1 - Prob. 27PPSCh. 11.1 - Prob. 28PPSCh. 11.1 - Prob. 29PPSCh. 11.1 - Prob. 30PPSCh. 11.1 - Prob. 31PPSCh. 11.1 - Prob. 32PPSCh. 11.1 - Prob. 33PPSCh. 11.1 - Prob. 34PPSCh. 11.1 - Prob. 35PPSCh. 11.1 - Prob. 36PPSCh. 11.1 - Prob. 37PPSCh. 11.1 - Prob. 38PPSCh. 11.1 - Prob. 39PPSCh. 11.1 - Prob. 40PPSCh. 11.1 - Prob. 41PPSCh. 11.1 - Prob. 42PPSCh. 11.1 - Prob. 43PPSCh. 11.1 - Prob. 44PPSCh. 11.1 - Prob. 45PPSCh. 11.1 - Prob. 46PPSCh. 11.1 - 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Prob. 50STPCh. 11.7 - Prob. 51SCh. 11.7 - Prob. 52SCh. 11.7 - Prob. 53SCh. 11.7 - Prob. 54SCh. 11.7 - Prob. 55SCh. 11.7 - Prob. 56SCh. 11.7 - Prob. 57SCh. 11.7 - Prob. 58SCh. 11.7 - Prob. 59SCh. 11.7 - Prob. 60SCh. 11.7 - Prob. 61SCh. 11.7 - Prob. 62SCh. 11 - Prob. 1QCCh. 11 - Prob. 2QCCh. 11 - Prob. 3QCCh. 11 - Prob. 4QCCh. 11 - Prob. 5QCCh. 11 - Prob. 6QCCh. 11 - Prob. 7QCCh. 11 - Prob. 8QCCh. 11 - Prob. 9QCCh. 11 - Prob. 10QCCh. 11 - Prob. 11QCCh. 11 - Prob. 12QCCh. 11 - Prob. 13QCCh. 11 - Prob. 14QCCh. 11 - Prob. 1MCQCh. 11 - Prob. 2MCQCh. 11 - Prob. 3MCQCh. 11 - Prob. 4MCQCh. 11 - Prob. 5MCQCh. 11 - Prob. 6MCQCh. 11 - Prob. 7MCQCh. 11 - Prob. 8MCQCh. 11 - Prob. 9MCQCh. 11 - Prob. 10MCQCh. 11 - Prob. 11MCQCh. 11 - Prob. 12MCQCh. 11 - Prob. 13MCQCh. 11 - Prob. 14MCQCh. 11 - Prob. 15MCQCh. 11 - Prob. 16MCQCh. 11 - Prob. 17MCQCh. 11 - Prob. 18MCQCh. 11 - Prob. 19MCQCh. 11 - Prob. 20MCQCh. 11 - Prob. 1SGRCh. 11 - Prob. 2SGRCh. 11 - Prob. 3SGRCh. 11 - Prob. 4SGRCh. 11 - Prob. 5SGRCh. 11 - Prob. 6SGRCh. 11 - Prob. 7SGRCh. 11 - Prob. 8SGRCh. 11 - Prob. 9SGRCh. 11 - Prob. 10SGRCh. 11 - Prob. 11SGRCh. 11 - Prob. 12SGRCh. 11 - Prob. 13SGRCh. 11 - Prob. 14SGRCh. 11 - Prob. 15SGRCh. 11 - Prob. 16SGRCh. 11 - Prob. 17SGRCh. 11 - Prob. 18SGRCh. 11 - Prob. 19SGRCh. 11 - Prob. 20SGRCh. 11 - Prob. 21SGRCh. 11 - Prob. 22SGRCh. 11 - Prob. 23SGRCh. 11 - Prob. 24SGRCh. 11 - Prob. 25SGRCh. 11 - Prob. 26SGRCh. 11 - Prob. 27SGRCh. 11 - Prob. 28SGRCh. 11 - Prob. 29SGRCh. 11 - Prob. 30SGRCh. 11 - Prob. 31SGRCh. 11 - Prob. 32SGRCh. 11 - Prob. 33SGRCh. 11 - Prob. 34SGRCh. 11 - Prob. 35SGRCh. 11 - Prob. 36SGRCh. 11 - Prob. 37SGRCh. 11 - Prob. 38SGRCh. 11 - Prob. 39SGRCh. 11 - Prob. 40SGRCh. 11 - Prob. 41SGRCh. 11 - Prob. 42SGRCh. 11 - Prob. 43SGRCh. 11 - Prob. 44SGRCh. 11 - Prob. 45SGRCh. 11 - Prob. 46SGRCh. 11 - Prob. 47SGRCh. 11 - Prob. 48SGRCh. 11 - Prob. 49SGRCh. 11 - Prob. 50SGRCh. 11 - Prob. 51SGRCh. 11 - Prob. 52SGRCh. 11 - Prob. 53SGRCh. 11 - Prob. 54SGRCh. 11 - Prob. 55SGRCh. 11 - Prob. 56SGRCh. 11 - Prob. 57SGRCh. 11 - Prob. 58SGRCh. 11 - Prob. 59SGRCh. 11 - Prob. 60SGRCh. 11 - Prob. 61SGRCh. 11 - Prob. 62SGRCh. 11 - Prob. 63SGRCh. 11 - Prob. 64SGRCh. 11 - Prob. 65SGRCh. 11 - Prob. 66SGRCh. 11 - Prob. 67SGRCh. 11 - Prob. 68SGRCh. 11 - Prob. 69SGRCh. 11 - Prob. 1PTCh. 11 - Prob. 2PTCh. 11 - Prob. 3PTCh. 11 - Prob. 4PTCh. 11 - Prob. 5PTCh. 11 - Prob. 6PTCh. 11 - Prob. 7PTCh. 11 - Prob. 8PTCh. 11 - Prob. 9PTCh. 11 - Prob. 10PTCh. 11 - Prob. 11PTCh. 11 - Prob. 12PTCh. 11 - Prob. 13PTCh. 11 - Prob. 14PTCh. 11 - Prob. 15PTCh. 11 - Prob. 16PTCh. 11 - Prob. 17PTCh. 11 - Prob. 18PTCh. 11 - Prob. 19PTCh. 11 - Prob. 20PTCh. 11 - Prob. 21PTCh. 11 - Prob. 22PTCh. 11 - Prob. 23PTCh. 11 - Prob. 24PTCh. 11 - Prob. 1ECh. 11 - Prob. 2ECh. 11 - Prob. 1STPCh. 11 - Prob. 2STPCh. 11 - Prob. 3STPCh. 11 - Prob. 4STPCh. 11 - Prob. 5STPCh. 11 - Prob. 6STPCh. 11 - Prob. 7STPCh. 11 - Prob. 8STPCh. 11 - Prob. 9STPCh. 11 - Prob. 10STPCh. 11 - Prob. 11STPCh. 11 - Prob. 12STPCh. 11 - Prob. 13STPCh. 11 - Prob. 14STPCh. 11 - Prob. 15STPCh. 11 - Prob. 16STPCh. 11 - Prob. 17STPCh. 11 - Prob. 18STP
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