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Arithmetic Sequences: Understanding the Concept and Finding the Equation of a Sequence, Lecture notes of Algebra

California College of the Arts (CAA)Algebra

An introduction to arithmetic sequences, explaining the definition, identifying examples, and demonstrating methods to find the equation of an arithmetic sequence. Students will learn how to determine the common difference, write the equation for the nth term, and find arithmetic means. The document also includes exercises to practice these concepts.

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

ekansh
ekansh 🇺🇸

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bg1
11.2ArithmeticSequencesDay1
1
Algebra2Intensified
:11.2Day1Notes–ArithmeticSequences
Definition:
An
arithmeticsequence
isasequenceinwhicheach
termafterthefirstisfoundbyaddingaconstant,calledthe
common
difference
,
d
,tothepreviousterm.
Example1
:

Fillinthenext3terms.Whatisthecommon
difference?
2,5,8,11,14,17,____,____,____
Example2
:

Fillinthenext3terms.Whatisthecommon
difference?
55,49,43,____,____,____
Formulaforwritinganequationofanarithmeticsequence:
Thenthtermofanarithmeticsequencewithfirst
termandcommondifferenceisgivenby
whereisanypositiveinteger.(*standsforthe
numberoftermsinthesequence)
Example3:
Writeanequationforthenthtermofthe
arithmeticsequence8,17,26,35,…
Method1:
1
st
findand.
2
nd
substituteandinto.
3
rd
simplify.
Method2:
Arithmeticsequencesarelinearsoyoucanfindthe
equationusing.
Example4:
a)Useeithermethodtofindtheequationforthe
nthtermofarithmeticsequence
b)Find
c)Findthe120
th
term.
Example5:
Findthe4arithmeticmeansbetween16and91.
(thismeansthe4missingtermsbetween16&91)
Method1:
Method2:
Example6:

Givenand,findtheequationof
thearithmeticsequenceandfindthe3arithmeticmeansbetween
them.
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11.2 Arithmetic Sequences Day 1

Algebra 2 Intensified: 11.2 Day 1 Notes – Arithmetic Sequences Definition: An arithmetic sequence is a sequence in which each term after the first is found by adding a constant, called the common difference , d , to the previous term. Example 1 : Fill in the next 3 terms. What is the common difference? 2, 5, 8, 11, 14, 17, ____, ____, ____ Example 2 : Fill in the next 3 terms. What is the common difference? 55, 49, 43, ____, ____, ____ Formula for writing an equation of an arithmetic sequence:

The nth term of an arithmetic sequence with first

term and common difference is given by

where is any positive integer. (* stands for the

number of terms in the sequence)

Example 3: Write an equation for the nth term of the arithmetic sequence 8, 17, 26, 35, … Method 1: 1 st^ find and. 2 nd^ substitute and into. 3 rd^ simplify. Method 2: Arithmetic sequences are linear so you can find the equation using. Example 4: a) Use either method to find the equation for the nth term of arithmetic sequence b) Find c) Find the 120 th^ term. Example 5: Find the 4 arithmetic means between 16 and 91. (this means the 4 missing terms between 16 & 91) Method 1: Method 2: Example 6: Given and , find the equation of the arithmetic sequence and find the 3 arithmetic means between them.

11.2 Arithmetic Sequences Day 1

Example 7: The table below shows typical costs for a construction company to rent a crane for one, two, three, or four months. Assuming that the arithmetic sequence continues, how much would it cost to rent a crane for 1 year? Months Cost 1 $75, 2 $90, 3 $105, 4 $120,