Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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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 3.5, Problem 24PPS

(a)

To determine

List the five terms

(a)

Expert Solution
Check Mark

Answer to Problem 24PPS

The first five terms of arithmetic sequence are − 3, − 1, 1, 3 and 5.

Explanation of Solution

Given:

The points on the graph are (1, − 3); (2, − 1); (3, 1); (4, 3); (5, 5)

Concept Used:

The points on the graph are (1, − 3); (2, − 1); (3, 1); (4, 3); (5, 5).

Because the terms are the second coordinate (y − coordinate) in each coordinate pair.

The terms of arithmetic sequence are − 3, − 1, 1, 3 and 5.

Calculation:

The points on the graph are (1, − 3); (2, − 1); (3, 1); (4, 3); (5, 5)

The first five terms of arithmetic sequence are − 3, − 1, 1, 3 and 5.

Thus, the first five terms of arithmetic sequence are − 3, − 1, 1, 3 and 5.

(b)

To determine

Write the formula for the nth term.

(b)

Expert Solution
Check Mark

Answer to Problem 24PPS

  an  =   2n−5

Explanation of Solution

Given:

The points on the graph are (1, − 3); (2, − 1); (3, 1); (4, 3); (5, 5)

Concept Used:

The first five terms of arithmetic sequence are − 3, − 1, 1, 3 and 5.

Find the common difference and find the nth term of the sequence.

Calculation:

Find the common difference: −1  −  (  −3)  =  −1  +3  =2

Write the equation for the nth terms of an arithmetic sequence by using the first term − 3 and common difference 2.

  a1  =   −3;    d=2

  an  =  a1  +  (n−1) d                      Formula  for  the  nth  term an  =  −3    +  (n−1  )  ·  2          a1=−3  and   d  =  2an  =   −3   +2n −2                       Distributive  Propertyan  =   2n−5                                Simplif

So, the formula for the nth terms of the arithmetic sequence is an  =   2n−5

Thus, the formula for the nth terms of the arithmetic sequence is an  =   2n−5

(c)

To determine

Write the function.

(c)

Expert Solution
Check Mark

Answer to Problem 24PPS

  f(n)=2n−5

Explanation of Solution

Given:

The points on the graph are (1, − 3); (2, − 1); (3, 1); (4, 3); (5, 5)

Concept Used:

The first five terms of arithmetic sequence are − 3, − 1, 1, 3 and 5.

The nth terms of the arithmetic sequence is an  =   2n−5

Formula for the nth term of the sequence is the function.

  f(n)=2n−5

Thus, the function is f(n)=2n−5

Previous
Chapter 3.5, Problem 23PPS
Next
Chapter 3.5, Problem 25PPS

Chapter 3 Solutions

Algebra 1

Ch. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 58PPSCh. 3.1 - Prob. 60HPCh. 3.1 - Prob. 68STPCh. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2CYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYP
Ch. 3.1 - Prob. 5ACYPCh. 3.1 - Prob. 5BCYPCh. 3.1 - Prob. 5CCYPCh. 3.1 - Prob. 1CYUCh. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13PPSCh. 3.1 - Prob. 14PPSCh. 3.1 - Prob. 15PPSCh. 3.1 - Prob. 16PPSCh. 3.1 - Prob. 17PPSCh. 3.1 - Prob. 18PPSCh. 3.1 - Prob. 19PPSCh. 3.1 - Prob. 20PPSCh. 3.1 - Prob. 21PPSCh. 3.1 - Prob. 22PPSCh. 3.1 - Prob. 23PPSCh. 3.1 - Prob. 24PPSCh. 3.1 - Prob. 25PPSCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42PPSCh. 3.1 - Prob. 43PPSCh. 3.1 - Prob. 44PPSCh. 3.1 - Prob. 45PPSCh. 3.1 - Prob. 46PPSCh. 3.1 - Prob. 47PPSCh. 3.1 - Prob. 48PPSCh. 3.1 - Prob. 49PPSCh. 3.1 - Prob. 50PPSCh. 3.1 - Prob. 51PPSCh. 3.1 - Prob. 52PPSCh. 3.1 - Prob. 53PPSCh. 3.1 - Prob. 54PPSCh. 3.1 - Prob. 55PPSCh. 3.1 - Prob. 56PPSCh. 3.1 - Prob. 57PPSCh. 3.1 - Prob. 59HPCh. 3.1 - Prob. 61HPCh. 3.1 - Prob. 62HPCh. 3.1 - Prob. 63HPCh. 3.1 - Prob. 64HPCh. 3.1 - Prob. 65STPCh. 3.1 - Prob. 66STPCh. 3.1 - Prob. 67STPCh. 3.1 - Prob. 69SRCh. 3.1 - Prob. 70SRCh. 3.1 - Prob. 71SRCh. 3.1 - Prob. 72SRCh. 3.1 - Prob. 73SRCh. 3.1 - Prob. 74SCh. 3.1 - Prob. 75SCh. 3.1 - Prob. 76SCh. 3.1 - Prob. 77SCh. 3.2 - Prob. 3CYPCh. 3.2 - Prob. 9CYUCh. 3.2 - Prob. 22PPSCh. 3.2 - Prob. 23PPSCh. 3.2 - Prob. 37PPSCh. 3.2 - Prob. 44PPSCh. 3.2 - Prob. 45PPSCh. 3.2 - Prob. 53STPCh. 3.2 - Prob. 1ACYPCh. 3.2 - Prob. 1BCYPCh. 3.2 - Prob. 2ACYPCh. 3.2 - Prob. 2BCYPCh. 3.2 - Prob. 1CYUCh. 3.2 - Prob. 2CYUCh. 3.2 - Prob. 3CYUCh. 3.2 - Prob. 4CYUCh. 3.2 - Prob. 5CYUCh. 3.2 - Prob. 6CYUCh. 3.2 - Prob. 7CYUCh. 3.2 - Prob. 8CYUCh. 3.2 - Prob. 10PPSCh. 3.2 - Prob. 11PPSCh. 3.2 - Prob. 12PPSCh. 3.2 - Prob. 13PPSCh. 3.2 - Prob. 14PPSCh. 3.2 - Prob. 15PPSCh. 3.2 - Prob. 16PPSCh. 3.2 - Prob. 17PPSCh. 3.2 - Prob. 18PPSCh. 3.2 - Prob. 19PPSCh. 3.2 - Prob. 20PPSCh. 3.2 - Prob. 21PPSCh. 3.2 - Prob. 24PPSCh. 3.2 - Prob. 25PPSCh. 3.2 - Prob. 26PPSCh. 3.2 - Prob. 27PPSCh. 3.2 - Prob. 28PPSCh. 3.2 - Prob. 29PPSCh. 3.2 - Prob. 30PPSCh. 3.2 - Prob. 31PPSCh. 3.2 - Prob. 32PPSCh. 3.2 - Prob. 33PPSCh. 3.2 - Prob. 34PPSCh. 3.2 - Prob. 35PPSCh. 3.2 - Prob. 36PPSCh. 3.2 - Prob. 38PPSCh. 3.2 - Prob. 39PPSCh. 3.2 - Prob. 40PPSCh. 3.2 - Prob. 41PPSCh. 3.2 - Prob. 42PPSCh. 3.2 - Prob. 43PPSCh. 3.2 - Prob. 46HPCh. 3.2 - Prob. 47HPCh. 3.2 - Prob. 48HPCh. 3.2 - Prob. 49HPCh. 3.2 - Prob. 50HPCh. 3.2 - Prob. 51STPCh. 3.2 - Prob. 52STPCh. 3.2 - Prob. 54STPCh. 3.2 - Prob. 55SRCh. 3.2 - Prob. 56SRCh. 3.2 - Prob. 57SRCh. 3.2 - Prob. 58SRCh. 3.2 - Prob. 59SRCh. 3.2 - Prob. 60SRCh. 3.2 - Prob. 61SCh. 3.2 - Prob. 62SCh. 3.2 - Prob. 63SCh. 3.2 - Prob. 64SCh. 3.2 - Prob. 65SCh. 3.2 - Prob. 66SCh. 3.2 - Prob. 67SCh. 3.3 - Prob. 1ACYPCh. 3.3 - Prob. 1BCYPCh. 3.3 - Prob. 2CYPCh. 3.3 - Prob. 3ACYPCh. 3.3 - Prob. 3BCYPCh. 3.3 - Prob. 4ACYPCh. 3.3 - Prob. 4BCYPCh. 3.3 - Prob. 4CCYPCh. 3.3 - Prob. 4DCYPCh. 3.3 - Prob. 4ECYPCh. 3.3 - Prob. 4FCYPCh. 3.3 - Prob. 5ACYPCh. 3.3 - Prob. 5BCYPCh. 3.3 - Prob. 6ACYPCh. 3.3 - Prob. 6BCYPCh. 3.3 - Prob. 1CYUCh. 3.3 - Prob. 2CYUCh. 3.3 - Prob. 3CYUCh. 3.3 - Prob. 4CYUCh. 3.3 - Prob. 5CYUCh. 3.3 - Prob. 6CYUCh. 3.3 - Prob. 7CYUCh. 3.3 - Prob. 8CYUCh. 3.3 - Prob. 9CYUCh. 3.3 - Prob. 10CYUCh. 3.3 - Prob. 11CYUCh. 3.3 - Prob. 12CYUCh. 3.3 - Prob. 13CYUCh. 3.3 - Prob. 14PPSCh. 3.3 - Prob. 15PPSCh. 3.3 - Prob. 16PPSCh. 3.3 - Prob. 17PPSCh. 3.3 - Prob. 18PPSCh. 3.3 - Prob. 19PPSCh. 3.3 - Prob. 20PPSCh. 3.3 - Prob. 21PPSCh. 3.3 - Prob. 22PPSCh. 3.3 - Prob. 23PPSCh. 3.3 - Prob. 24PPSCh. 3.3 - Prob. 25PPSCh. 3.3 - Prob. 26PPSCh. 3.3 - Prob. 27PPSCh. 3.3 - Prob. 28PPSCh. 3.3 - Prob. 29PPSCh. 3.3 - Prob. 30PPSCh. 3.3 - Prob. 31PPSCh. 3.3 - Prob. 32PPSCh. 3.3 - 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Prob. 3CYUCh. 3.4 - Prob. 4CYUCh. 3.4 - Prob. 5CYUCh. 3.4 - Prob. 6CYUCh. 3.4 - Prob. 7CYUCh. 3.4 - Prob. 8CYUCh. 3.4 - Prob. 9CYUCh. 3.4 - Prob. 10PPSCh. 3.4 - Prob. 11PPSCh. 3.4 - Prob. 12PPSCh. 3.4 - Prob. 13PPSCh. 3.4 - Prob. 14PPSCh. 3.4 - Prob. 15PPSCh. 3.4 - Prob. 16PPSCh. 3.4 - Prob. 17PPSCh. 3.4 - Prob. 18PPSCh. 3.4 - Prob. 19PPSCh. 3.4 - Prob. 20PPSCh. 3.4 - Prob. 21PPSCh. 3.4 - Prob. 22PPSCh. 3.4 - Prob. 23PPSCh. 3.4 - Prob. 24PPSCh. 3.4 - Prob. 25PPSCh. 3.4 - Prob. 26PPSCh. 3.4 - Prob. 27PPSCh. 3.4 - Prob. 28PPSCh. 3.4 - Prob. 29PPSCh. 3.4 - Prob. 30PPSCh. 3.4 - Prob. 31PPSCh. 3.4 - Prob. 32PPSCh. 3.4 - Prob. 33PPSCh. 3.4 - Prob. 34PPSCh. 3.4 - Prob. 35PPSCh. 3.4 - Prob. 36PPSCh. 3.4 - Prob. 37PPSCh. 3.4 - Prob. 38PPSCh. 3.4 - Prob. 39PPSCh. 3.4 - Prob. 40PPSCh. 3.4 - Prob. 41PPSCh. 3.4 - Prob. 42PPSCh. 3.4 - Prob. 43PPSCh. 3.4 - Prob. 44PPSCh. 3.4 - Prob. 45HPCh. 3.4 - Prob. 46HPCh. 3.4 - Prob. 47HPCh. 3.4 - Prob. 48HPCh. 3.4 - Prob. 49HPCh. 3.4 - Prob. 50HPCh. 3.4 - Prob. 51STPCh. 3.4 - Prob. 52STPCh. 3.4 - Prob. 53STPCh. 3.4 - Prob. 54STPCh. 3.4 - Prob. 55SRCh. 3.4 - Prob. 56SRCh. 3.4 - Prob. 57SRCh. 3.4 - Prob. 58SRCh. 3.4 - Prob. 59SRCh. 3.4 - Prob. 60SRCh. 3.4 - Prob. 61SRCh. 3.4 - Prob. 62SRCh. 3.4 - Prob. 63SRCh. 3.4 - Prob. 64SRCh. 3.4 - Prob. 65SRCh. 3.4 - Prob. 66SRCh. 3.4 - Prob. 67SRCh. 3.4 - Prob. 68SCh. 3.4 - Prob. 69SCh. 3.4 - Prob. 70SCh. 3.4 - Prob. 71SCh. 3.4 - Prob. 72SCh. 3.4 - Prob. 73SCh. 3.5 - Prob. 1ACYPCh. 3.5 - Prob. 1BCYPCh. 3.5 - Prob. 2CYPCh. 3.5 - Prob. 3ACYPCh. 3.5 - Prob. 3BCYPCh. 3.5 - Prob. 3CCYPCh. 3.5 - Prob. 3DCYPCh. 3.5 - Prob. 4ACYPCh. 3.5 - Prob. 4BCYPCh. 3.5 - Prob. 1CYUCh. 3.5 - Prob. 2CYUCh. 3.5 - Prob. 3CYUCh. 3.5 - Prob. 4CYUCh. 3.5 - Prob. 5CYUCh. 3.5 - Prob. 6CYUCh. 3.5 - Prob. 7CYUCh. 3.5 - Prob. 8PPSCh. 3.5 - Prob. 9PPSCh. 3.5 - Prob. 10PPSCh. 3.5 - Prob. 11PPSCh. 3.5 - Prob. 12PPSCh. 3.5 - Prob. 13PPSCh. 3.5 - Prob. 14PPSCh. 3.5 - Prob. 15PPSCh. 3.5 - Prob. 16PPSCh. 3.5 - Prob. 17PPSCh. 3.5 - Prob. 18PPSCh. 3.5 - Prob. 19PPSCh. 3.5 - Prob. 20PPSCh. 3.5 - Prob. 21PPSCh. 3.5 - Prob. 22PPSCh. 3.5 - Prob. 23PPSCh. 3.5 - Prob. 24PPSCh. 3.5 - Prob. 25PPSCh. 3.5 - Prob. 26PPSCh. 3.5 - Prob. 27PPSCh. 3.5 - Prob. 28PPSCh. 3.5 - Prob. 29PPSCh. 3.5 - Prob. 30PPSCh. 3.5 - Prob. 32HPCh. 3.5 - Prob. 33HPCh. 3.5 - Prob. 34HPCh. 3.5 - Prob. 35HPCh. 3.5 - Prob. 36HPCh. 3.5 - Prob. 37STPCh. 3.5 - Prob. 38STPCh. 3.5 - Prob. 39STPCh. 3.5 - Prob. 40STPCh. 3.5 - Prob. 41SRCh. 3.5 - Prob. 42SRCh. 3.5 - Prob. 43SRCh. 3.5 - Prob. 44SRCh. 3.5 - Prob. 45SRCh. 3.5 - Prob. 46SRCh. 3.5 - Prob. 47SRCh. 3.5 - Prob. 48SRCh. 3.5 - Prob. 49SRCh. 3.5 - Prob. 50SCh. 3.5 - Prob. 51SCh. 3.5 - Prob. 52SCh. 3.5 - Prob. 53SCh. 3.5 - Prob. 54SCh. 3.5 - Prob. 55SCh. 3.5 - Prob. 31PPSCh. 3.6 - Prob. 2CYUCh. 3.6 - Prob. 3CYUCh. 3.6 - Prob. 5PPSCh. 3.6 - Prob. 6PPSCh. 3.6 - Prob. 7PPSCh. 3.6 - Prob. 8PPSCh. 3.6 - Prob. 9PPSCh. 3.6 - Prob. 10PPSCh. 3.6 - Prob. 1CYUCh. 3.6 - Prob. 4PPSCh. 3.6 - Prob. 11PPSCh. 3.6 - Prob. 12PPSCh. 3.6 - Prob. 13PPSCh. 3.6 - Prob. 14HPCh. 3.6 - Prob. 15HPCh. 3.6 - Prob. 16HPCh. 3.6 - Prob. 17HPCh. 3.6 - Prob. 18HPCh. 3.6 - Prob. 1ACYPCh. 3.6 - Prob. 1BCYPCh. 3.6 - Prob. 1CCYPCh. 3.6 - Prob. 2ACYPCh. 3.6 - Prob. 2BCYPCh. 3.6 - Prob. 19STPCh. 3.6 - Prob. 20STPCh. 3.6 - Prob. 21STPCh. 3.6 - Prob. 22STPCh. 3.6 - Prob. 23SRCh. 3.6 - Prob. 24SRCh. 3.6 - Prob. 25SRCh. 3.6 - Prob. 26SRCh. 3.6 - Prob. 27SRCh. 3.6 - Prob. 28SRCh. 3.6 - Prob. 29SRCh. 3.6 - Prob. 30SCh. 3.6 - Prob. 31SCh. 3.6 - Prob. 32SCh. 3.6 - Prob. 33SCh. 3.6 - Prob. 34SCh. 3.6 - Prob. 35SCh. 3 - Prob. 1QCCh. 3 - Prob. 2QCCh. 3 - Prob. 3QCCh. 3 - Prob. 4QCCh. 3 - Prob. 5QCCh. 3 - Prob. 6QCCh. 3 - Prob. 13QCCh. 3 - Prob. 14QCCh. 3 - Prob. 15QCCh. 3 - Prob. 16QCCh. 3 - Prob. 17QCCh. 3 - Prob. 18QCCh. 3 - Prob. 19QCCh. 3 - Prob. 20QCCh. 3 - Prob. 21QCCh. 3 - Prob. 22QCCh. 3 - Prob. 23QCCh. 3 - Prob. 1MCQCh. 3 - Prob. 2MCQCh. 3 - Prob. 3MCQCh. 3 - Prob. 4MCQCh. 3 - Prob. 5MCQCh. 3 - Prob. 6MCQCh. 3 - Prob. 9MCQCh. 3 - Prob. 10MCQCh. 3 - Prob. 11MCQCh. 3 - Prob. 12MCQCh. 3 - 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