Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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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
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Chapter 7.10, Problem 27PPS

a.

To determine

Find the first five term of the sequence representing the number of people who receive the photo in the nth round.

a.

Expert Solution
Check Mark

Answer to Problem 27PPS

The first five term of the sequence are 1,5,25,125,625.

Explanation of Solution

Given: PHOTO SHARING Barbara shares a photo with five of her friends. Each of her friends shared the photo with five more friends , and so on.

Calculation:

Initially ,only Barbara received the message so a1=1 . Barbara then shared it with 5 people received the photo in 2nd round which gives a2=5 . Those 5 people each shared it with 5 people so 5.5=25 people received the photo on the 3rd round which gives a3=25. The pattern is then multiplying by 5 so a4=5a3=5(25)=125.​ and a5=5(a4)=5(125)=625.

So, the first five term of the sequence are 1,5,25,125,625.

b.

To determine

Write a recursive formula for the sequence.

b.

Expert Solution
Check Mark

Answer to Problem 27PPS

  a1=1 , an=5an−1 , n≥2 .

Explanation of Solution

Given: PHOTO SHARING Barbara shares a photo with five of her friends. Each of her friends shared the photo with five more friends , and so on.

.

Calculation:

From part (a) , , the sequence is 1,5,25,125,625. So a1=1 and there is a common ratio of r =5. The recursive formula for geometric sequence is

  an=ran−1=5an−1. this formula is used to find the second term and on so it has a domain of n≥2. The answer is then,

  a1=1 , an=5an−1 , n≥2 .

c.

To determine

If Barbara represents a1 , find a8.

c.

Expert Solution
Check Mark

Answer to Problem 27PPS

  a8=78,125.

Explanation of Solution

Given: PHOTO SHARING Barbara shares a photo with five of her friends. Each of her friends shared the photo with five more friends, and so on.

Calculation:

From part (a) and (b) we know a1=1 and r=5 . Substituting these into the explicit formula for a geometric sequence gives:

  an=a1rn−1=1(5)n−1=5n−1Substituting n=8.a8=58−1=57=78,125.a8=78,125.

Conclusion:

  a8=78,125.

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Chapter 7.10, Problem 26PPS
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Chapter 7.10, Problem 28PPS

Chapter 7 Solutions

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Ch. 7.1 - Prob. 1AGPCh. 7.1 - Prob. 1BGPCh. 7.1 - Prob. 1CGPCh. 7.1 - Prob. 1DGPCh. 7.1 - Prob. 2AGPCh. 7.1 - Prob. 2BGPCh. 7.1 - Prob. 3GPCh. 7.1 - Prob. 4AGPCh. 7.1 - Prob. 4BGPCh. 7.1 - Prob. 5GP
Ch. 7.1 - Prob. 1CYUCh. 7.1 - Prob. 2CYUCh. 7.1 - Prob. 3CYUCh. 7.1 - Prob. 4CYUCh. 7.1 - Prob. 5CYUCh. 7.1 - Prob. 6CYUCh. 7.1 - Prob. 7CYUCh. 7.1 - Prob. 8CYUCh. 7.1 - Prob. 9CYUCh. 7.1 - Prob. 10CYUCh. 7.1 - Prob. 11CYUCh. 7.1 - Prob. 12CYUCh. 7.1 - Prob. 13CYUCh. 7.1 - Prob. 14CYUCh. 7.1 - Prob. 15CYUCh. 7.1 - Prob. 16CYUCh. 7.1 - Prob. 17CYUCh. 7.1 - Prob. 18CYUCh. 7.1 - Prob. 19CYUCh. 7.1 - Prob. 20CYUCh. 7.1 - Prob. 21PPSCh. 7.1 - Prob. 22PPSCh. 7.1 - Prob. 23PPSCh. 7.1 - Prob. 24PPSCh. 7.1 - Prob. 25PPSCh. 7.1 - Prob. 26PPSCh. 7.1 - Prob. 27PPSCh. 7.1 - Prob. 28PPSCh. 7.1 - Prob. 29PPSCh. 7.1 - Prob. 30PPSCh. 7.1 - Prob. 31PPSCh. 7.1 - Prob. 32PPSCh. 7.1 - Prob. 33PPSCh. 7.1 - Prob. 34PPSCh. 7.1 - Prob. 35PPSCh. 7.1 - Prob. 36PPSCh. 7.1 - Prob. 37PPSCh. 7.1 - Prob. 38PPSCh. 7.1 - Prob. 39PPSCh. 7.1 - Prob. 40PPSCh. 7.1 - Prob. 41PPSCh. 7.1 - Prob. 42PPSCh. 7.1 - Prob. 43PPSCh. 7.1 - Prob. 44PPSCh. 7.1 - Prob. 45PPSCh. 7.1 - Prob. 46PPSCh. 7.1 - Prob. 47PPSCh. 7.1 - Prob. 48PPSCh. 7.1 - 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Prob. 7CGPCh. 7.4 - Prob. 7DGPCh. 7.4 - Prob. 8AGPCh. 7.4 - Prob. 8BGPCh. 7.4 - Prob. 8CGPCh. 7.4 - Prob. 8DGPCh. 7.4 - Prob. 9GPCh. 7.4 - Prob. 1CYUCh. 7.4 - Prob. 2CYUCh. 7.4 - Prob. 3CYUCh. 7.4 - Prob. 4CYUCh. 7.4 - Prob. 5CYUCh. 7.4 - Prob. 6CYUCh. 7.4 - Prob. 7CYUCh. 7.4 - Prob. 8CYUCh. 7.4 - Prob. 9CYUCh. 7.4 - Prob. 10CYUCh. 7.4 - Prob. 11CYUCh. 7.4 - Prob. 12CYUCh. 7.4 - Prob. 13CYUCh. 7.4 - Prob. 14CYUCh. 7.4 - Prob. 15CYUCh. 7.4 - Prob. 16CYUCh. 7.4 - Prob. 17CYUCh. 7.4 - Prob. 18CYUCh. 7.4 - Prob. 19CYUCh. 7.4 - Prob. 20CYUCh. 7.4 - Prob. 21CYUCh. 7.4 - Prob. 22CYUCh. 7.4 - Prob. 23CYUCh. 7.4 - Prob. 24CYUCh. 7.4 - Prob. 25CYUCh. 7.4 - Prob. 26CYUCh. 7.4 - Prob. 27CYUCh. 7.4 - Prob. 28CYUCh. 7.4 - Prob. 29CYUCh. 7.4 - Prob. 30PPSCh. 7.4 - Prob. 31PPSCh. 7.4 - Prob. 32PPSCh. 7.4 - Prob. 33PPSCh. 7.4 - Prob. 34PPSCh. 7.4 - Prob. 35PPSCh. 7.4 - Prob. 36PPSCh. 7.4 - Prob. 37PPSCh. 7.4 - Prob. 38PPSCh. 7.4 - Prob. 39PPSCh. 7.4 - Prob. 40PPSCh. 7.4 - Prob. 41PPSCh. 7.4 - Prob. 42PPSCh. 7.4 - 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Prob. 3GPCh. 7.5 - Prob. 4GPCh. 7.5 - Prob. 1CYUCh. 7.5 - Prob. 2CYUCh. 7.5 - Prob. 3CYUCh. 7.5 - Prob. 4CYUCh. 7.5 - Prob. 5CYUCh. 7.5 - Prob. 6CYUCh. 7.5 - Prob. 7CYUCh. 7.5 - Prob. 8CYUCh. 7.5 - Prob. 9CYUCh. 7.5 - Prob. 10PPSCh. 7.5 - Prob. 11PPSCh. 7.5 - Prob. 12PPSCh. 7.5 - Prob. 13PPSCh. 7.5 - Prob. 14PPSCh. 7.5 - Prob. 15PPSCh. 7.5 - Prob. 16PPSCh. 7.5 - Prob. 17PPSCh. 7.5 - Prob. 18PPSCh. 7.5 - Prob. 19PPSCh. 7.5 - Prob. 20PPSCh. 7.5 - Prob. 21PPSCh. 7.5 - Prob. 22PPSCh. 7.5 - Prob. 23PPSCh. 7.5 - Prob. 24PPSCh. 7.5 - Prob. 25PPSCh. 7.5 - Prob. 26PPSCh. 7.5 - Prob. 27PPSCh. 7.5 - Prob. 28PPSCh. 7.5 - Prob. 29PPSCh. 7.5 - Prob. 30PPSCh. 7.5 - Prob. 31PPSCh. 7.5 - Prob. 32PPSCh. 7.5 - Prob. 33PPSCh. 7.5 - Prob. 34PPSCh. 7.5 - Prob. 35PPSCh. 7.5 - Prob. 36PPSCh. 7.5 - Prob. 37PPSCh. 7.5 - Prob. 38PPSCh. 7.5 - Prob. 39PPSCh. 7.5 - Prob. 40PPSCh. 7.5 - Prob. 41HPCh. 7.5 - Prob. 42HPCh. 7.5 - Prob. 43HPCh. 7.5 - Prob. 44HPCh. 7.5 - Prob. 45HPCh. 7.5 - Prob. 46PFACh. 7.5 - Prob. 47PFACh. 7.5 - 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Prob. 4CYUCh. 7.7 - Prob. 5CYUCh. 7.7 - Prob. 6CYUCh. 7.7 - Prob. 7CYUCh. 7.7 - Prob. 8CYUCh. 7.7 - Prob. 9PPSCh. 7.7 - Prob. 10PPSCh. 7.7 - Prob. 11PPSCh. 7.7 - Prob. 12PPSCh. 7.7 - Prob. 13PPSCh. 7.7 - Prob. 14PPSCh. 7.7 - Prob. 15PPSCh. 7.7 - Prob. 16PPSCh. 7.7 - Prob. 17PPSCh. 7.7 - Prob. 18PPSCh. 7.7 - Prob. 19PPSCh. 7.7 - Prob. 20PPSCh. 7.7 - Prob. 21PPSCh. 7.7 - Prob. 22PPSCh. 7.7 - Prob. 23PPSCh. 7.7 - Prob. 24PPSCh. 7.7 - Prob. 25PPSCh. 7.7 - Prob. 26PPSCh. 7.7 - Prob. 27PPSCh. 7.7 - Prob. 28PPSCh. 7.7 - Prob. 29PPSCh. 7.7 - Prob. 30HPCh. 7.7 - Prob. 31HPCh. 7.7 - Prob. 32HPCh. 7.7 - Prob. 33HPCh. 7.7 - Prob. 34HPCh. 7.7 - Prob. 35PFACh. 7.7 - Prob. 36PFACh. 7.7 - Prob. 37PFACh. 7.7 - Prob. 38PFACh. 7.7 - Prob. 39PFACh. 7.7 - Prob. 40PFACh. 7.7 - Prob. 41PFACh. 7.7 - Prob. 42PFACh. 7.8 - Prob. 1GPCh. 7.8 - Prob. 2GPCh. 7.8 - Prob. 1CYUCh. 7.8 - Prob. 2CYUCh. 7.8 - Prob. 3PPSCh. 7.8 - Prob. 4PPSCh. 7.8 - Prob. 5PPSCh. 7.8 - Prob. 6PPSCh. 7.8 - Prob. 7PPSCh. 7.8 - Prob. 8HPCh. 7.8 - Prob. 9HPCh. 7.8 - Prob. 10HPCh. 7.8 - Prob. 11HPCh. 7.8 - Prob. 12PFACh. 7.8 - Prob. 13PFACh. 7.8 - Prob. 14PFACh. 7.8 - Prob. 15PFACh. 7.8 - Prob. 16PFACh. 7.8 - Prob. 17PFACh. 7.8 - Prob. 18PFACh. 7.9 - Prob. 1AGPCh. 7.9 - Prob. 1BGPCh. 7.9 - Prob. 1CGPCh. 7.9 - Prob. 2AGPCh. 7.9 - Prob. 2BGPCh. 7.9 - Prob. 3GPCh. 7.9 - Prob. 4GPCh. 7.9 - Prob. 1CYUCh. 7.9 - Prob. 2CYUCh. 7.9 - Prob. 3CYUCh. 7.9 - Prob. 4CYUCh. 7.9 - Prob. 5CYUCh. 7.9 - Prob. 6CYUCh. 7.9 - Prob. 7CYUCh. 7.9 - Prob. 8CYUCh. 7.9 - Prob. 9CYUCh. 7.9 - Prob. 10CYUCh. 7.9 - Prob. 11CYUCh. 7.9 - Prob. 12CYUCh. 7.9 - Prob. 13CYUCh. 7.9 - Prob. 14PPSCh. 7.9 - Prob. 15PPSCh. 7.9 - Prob. 16PPSCh. 7.9 - Prob. 17PPSCh. 7.9 - Prob. 18PPSCh. 7.9 - Prob. 19PPSCh. 7.9 - Prob. 20PPSCh. 7.9 - Prob. 21PPSCh. 7.9 - Prob. 22PPSCh. 7.9 - Prob. 23PPSCh. 7.9 - Prob. 24PPSCh. 7.9 - Prob. 25PPSCh. 7.9 - Prob. 26PPSCh. 7.9 - Prob. 27PPSCh. 7.9 - Prob. 28PPSCh. 7.9 - Prob. 29PPSCh. 7.9 - Prob. 30PPSCh. 7.9 - Prob. 31PPSCh. 7.9 - Prob. 32PPSCh. 7.9 - Prob. 33PPSCh. 7.9 - Prob. 34PPSCh. 7.9 - Prob. 35PPSCh. 7.9 - Prob. 36PPSCh. 7.9 - Prob. 37PPSCh. 7.9 - Prob. 38HPCh. 7.9 - Prob. 39HPCh. 7.9 - Prob. 40HPCh. 7.9 - Prob. 41HPCh. 7.9 - Prob. 42HPCh. 7.9 - Prob. 43PFACh. 7.9 - Prob. 44PFACh. 7.9 - Prob. 45PFACh. 7.9 - Prob. 46PFACh. 7.9 - Prob. 47PFACh. 7.9 - Prob. 48PFACh. 7.9 - Prob. 49PFACh. 7.10 - Prob. 1AGPCh. 7.10 - Prob. 1BGPCh. 7.10 - Prob. 2GPCh. 7.10 - Prob. 3GPCh. 7.10 - Prob. 4AGPCh. 7.10 - Prob. 4BGPCh. 7.10 - Prob. 1CYUCh. 7.10 - Prob. 2CYUCh. 7.10 - Prob. 3CYUCh. 7.10 - Prob. 4CYUCh. 7.10 - Prob. 5CYUCh. 7.10 - Prob. 6CYUCh. 7.10 - Prob. 7CYUCh. 7.10 - Prob. 8CYUCh. 7.10 - Prob. 9CYUCh. 7.10 - Prob. 10PPSCh. 7.10 - Prob. 11PPSCh. 7.10 - Prob. 12PPSCh. 7.10 - Prob. 13PPSCh. 7.10 - Prob. 14PPSCh. 7.10 - Prob. 15PPSCh. 7.10 - Prob. 16PPSCh. 7.10 - Prob. 17PPSCh. 7.10 - Prob. 18PPSCh. 7.10 - Prob. 19PPSCh. 7.10 - Prob. 20PPSCh. 7.10 - Prob. 21PPSCh. 7.10 - Prob. 22PPSCh. 7.10 - Prob. 23PPSCh. 7.10 - Prob. 24PPSCh. 7.10 - Prob. 25PPSCh. 7.10 - Prob. 26PPSCh. 7.10 - Prob. 27PPSCh. 7.10 - Prob. 28PPSCh. 7.10 - Prob. 29PPSCh. 7.10 - Prob. 30PPSCh. 7.10 - Prob. 31HPCh. 7.10 - Prob. 32HPCh. 7.10 - Prob. 33HPCh. 7.10 - Prob. 34HPCh. 7.10 - Prob. 35HPCh. 7.10 - Prob. 36PFACh. 7.10 - Prob. 37PFACh. 7.10 - Prob. 38PFACh. 7.10 - Prob. 39PFACh. 7.10 - Prob. 40PFACh. 7 - Prob. 1MCQCh. 7 - Prob. 2MCQCh. 7 - Prob. 3MCQCh. 7 - Prob. 4MCQCh. 7 - Prob. 5MCQCh. 7 - Prob. 6MCQCh. 7 - Prob. 7MCQCh. 7 - Prob. 8MCQCh. 7 - Prob. 9MCQCh. 7 - Prob. 10MCQCh. 7 - Prob. 11MCQCh. 7 - Prob. 12MCQCh. 7 - Prob. 13MCQCh. 7 - Prob. 14MCQCh. 7 - Prob. 15MCQCh. 7 - Prob. 16MCQCh. 7 - Prob. 17MCQCh. 7 - Prob. 18MCQCh. 7 - Prob. 19MCQCh. 7 - Prob. 20MCQCh. 7 - Prob. 21MCQCh. 7 - Prob. 22MCQCh. 7 - Prob. 23MCQCh. 7 - Prob. 24MCQCh. 7 - Prob. 25MCQCh. 7 - Prob. 26MCQCh. 7 - Prob. 27MCQCh. 7 - Prob. 1SGRCh. 7 - Prob. 2SGRCh. 7 - Prob. 3SGRCh. 7 - Prob. 4SGRCh. 7 - Prob. 5SGRCh. 7 - Prob. 6SGRCh. 7 - Prob. 7SGRCh. 7 - Prob. 8SGRCh. 7 - Prob. 9SGRCh. 7 - Prob. 10SGRCh. 7 - Prob. 11SGRCh. 7 - Prob. 12SGRCh. 7 - Prob. 13SGRCh. 7 - Prob. 14SGRCh. 7 - Prob. 15SGRCh. 7 - Prob. 16SGRCh. 7 - Prob. 17SGRCh. 7 - Prob. 18SGRCh. 7 - Prob. 19SGRCh. 7 - Prob. 20SGRCh. 7 - Prob. 21SGRCh. 7 - Prob. 22SGRCh. 7 - Prob. 23SGRCh. 7 - Prob. 24SGRCh. 7 - Prob. 25SGRCh. 7 - Prob. 26SGRCh. 7 - Prob. 27SGRCh. 7 - Prob. 28SGRCh. 7 - Prob. 29SGRCh. 7 - Prob. 30SGRCh. 7 - Prob. 31SGRCh. 7 - Prob. 32SGRCh. 7 - Prob. 33SGRCh. 7 - Prob. 34SGRCh. 7 - Prob. 35SGRCh. 7 - Prob. 36SGRCh. 7 - Prob. 37SGRCh. 7 - Prob. 38SGRCh. 7 - Prob. 39SGRCh. 7 - Prob. 40SGRCh. 7 - Prob. 41SGRCh. 7 - Prob. 42SGRCh. 7 - Prob. 43SGRCh. 7 - Prob. 44SGRCh. 7 - Prob. 45SGRCh. 7 - Prob. 46SGRCh. 7 - Prob. 47SGRCh. 7 - Prob. 48SGRCh. 7 - Prob. 49SGRCh. 7 - Prob. 50SGRCh. 7 - Prob. 51SGRCh. 7 - Prob. 52SGRCh. 7 - Prob. 53SGRCh. 7 - Prob. 54SGRCh. 7 - Prob. 55SGRCh. 7 - Prob. 56SGRCh. 7 - Prob. 57SGRCh. 7 - Prob. 58SGRCh. 7 - Prob. 59SGRCh. 7 - Prob. 60SGRCh. 7 - Prob. 61SGRCh. 7 - Prob. 62SGRCh. 7 - Prob. 63SGRCh. 7 - Prob. 64SGRCh. 7 - Prob. 65SGRCh. 7 - Prob. 66SGRCh. 7 - Prob. 67SGRCh. 7 - Prob. 68SGRCh. 7 - Prob. 69SGRCh. 7 - Prob. 70SGRCh. 7 - Prob. 71SGRCh. 7 - Prob. 72SGRCh. 7 - Prob. 73SGRCh. 7 - Prob. 74SGRCh. 7 - Prob. 75SGRCh. 7 - Prob. 76SGRCh. 7 - Prob. 77SGRCh. 7 - Prob. 78SGRCh. 7 - Prob. 79SGRCh. 7 - Prob. 80SGRCh. 7 - Prob. 81SGRCh. 7 - Prob. 1PTCh. 7 - Prob. 2PTCh. 7 - Prob. 3PTCh. 7 - Prob. 4PTCh. 7 - Prob. 5PTCh. 7 - Prob. 6PTCh. 7 - Prob. 7PTCh. 7 - Prob. 8PTCh. 7 - Prob. 9PTCh. 7 - Prob. 10PTCh. 7 - Prob. 11PTCh. 7 - Prob. 12PTCh. 7 - Prob. 13PTCh. 7 - Prob. 14PTCh. 7 - Prob. 15PTCh. 7 - Prob. 16PTCh. 7 - Prob. 17PTCh. 7 - Prob. 18PTCh. 7 - Prob. 19PTCh. 7 - Prob. 20PTCh. 7 - Prob. 21PTCh. 7 - Prob. 22PTCh. 7 - Prob. 23PTCh. 7 - Prob. 24PTCh. 7 - Prob. 25PTCh. 7 - Prob. 26PTCh. 7 - Prob. 27PTCh. 7 - Prob. 28PTCh. 7 - Prob. 29PTCh. 7 - Prob. 30PTCh. 7 - Prob. 31PTCh. 7 - Prob. 32PTCh. 7 - Prob. 33PTCh. 7 - Prob. 34PTCh. 7 - Prob. 35PTCh. 7 - Prob. 36PTCh. 7 - Prob. 37PTCh. 7 - Prob. 1PFACh. 7 - Prob. 2PFACh. 7 - Prob. 3PFACh. 7 - Prob. 4PFACh. 7 - Prob. 5PFACh. 7 - Prob. 6PFACh. 7 - Prob. 7PFACh. 7 - Prob. 8PFACh. 7 - Prob. 9PFACh. 7 - Prob. 10PFACh. 7 - Prob. 11PFACh. 7 - Prob. 12PFACh. 7 - Prob. 13PFACh. 7 - Prob. 14PFACh. 7 - Prob. 15PFA

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