MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C957DD.1F8C5810" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences

This presentation contains content that your browser may not be able to = show properly. This presentation was optimized for more recent versions of Micro= soft Internet Explorer.

If you would like to proceed anyway, click here.

 ------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/master08.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
Click to edit Master title style
Clic= k to edit Master text styles
Sec= ond level
Thi= rd level
Fou= rth level
Fif= th level
‹date/time›
‹footer›
‹#›
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/master08.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD1QAAAAYAJQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAHAAAA/AIAAP///wAAAAQAAAAtAQMABAAA ACcB//8cAAAA+wLU/wAAAAAAAJABAAAAAABAACJBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAQAAAAtAQQABAAAAC4BGAAEAAAAAgEBAAUAAAAJAgAAAAIlAAAAMgowACgBFAAAAEFyaXRo bWV0aWMgU2VxdWVuY2VzHQAPAAoADAAYACYAGAAMAAoAFwAMAB4AGAAZABkAGQAYABcAGAAWAAQA AAAuAQAAHAAAAPsCEAAHAAAAAAC8AgAAAAABAgIiU3lzdGVtAAAAAAAAGAAAACyeEwACAAAA5AQA AAAAAAAEAAAALQEFAAQAAADwAQQAAwAAAAAA ------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0136.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
A sequence a1, a2 , a3 , … is an arithmetic sequence
if an =3D= d*n + c, i.e. it is defined by a linear formula.
Arithmetic Seque= nces <= /div>
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0137.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
A sequence a1, a2 , a3 , … is an arithmetic sequence
if an =3D= d*n + c, i.e. it is defined by a linear formula.
Example A. The sequence of odd numbers
a1=3D 1, a2=3D 3, a3=3D 5, a4=3D 7, R= 30;
is an arithmetic sequence because an =3D 2n – 1.
Arithmetic Seque= nces <= /div>
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0138.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
A sequence a1, a2 , a3 , … is an arithmetic sequence
if an =3D= d*n + c, i.e. it is defined by a linear formula.
Example A. The sequence of odd numbers
a1=3D 1, a2=3D 3, a3=3D 5, a4=3D 7, R= 30;
is an arithmetic sequence because an =3D 2n – 1.
Fact: If a1, a= 2 , a3 , …is an arithmetic seque= nce and that
an =3D d*n + c  then the difference between any t= wo terms is d, &= #13;
i.e. ak+1 – ak =3D= d.
Arithmetic Seque= nces <= /div>
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0139.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
A sequence a1, a2 , a3 , … is an arithmetic sequence
if an =3D= d*n + c, i.e. it is defined by a linear formula.
Example A. The sequence of odd numbers
a1=3D 1, a2=3D 3, a3=3D 5, a4=3D 7, R= 30;
is an arithmetic sequence because an =3D 2n – 1.
Fact: If a1, a= 2 , a3 , …is an arithmetic seque= nce and that
an =3D d*n + c  then the difference between any t= wo terms is d, &= #13;
i.e. ak+1 – ak =3D= d.
Arithmetic Seque= nces <= /div>
In example A, 3 – 1= =3D 5 – 3 =3D 7 – 5 =3D 2 = =3D d.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0140.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
A sequence a1, a2 , a3 , … is an arithmetic sequence
if an =3D= d*n + c, i.e. it is defined by a linear formula.
Example A. The sequence of odd numbers
a1=3D 1, a2=3D 3, a3=3D 5, a4=3D 7, R= 30;
is an arithmetic sequence because an =3D 2n – 1.
Fact: If a1, a= 2 , a3 , …is an arithmetic seque= nce and that
an =3D d*n + c  then the difference between any t= wo terms is d, &= #13;
i.e. ak+1 – ak =3D= d.
Arithmetic Seque= nces <= /div>
The following theorem gives the converse of the above fact
and the main formula for arithm= etic sequences. 
In example A, 3 – 1= =3D 5 – 3 =3D 7 – 5 =3D 2 = =3D d.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0141.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
A sequence a1, a2 , a3 , … is an arithmetic sequence
if an =3D= d*n + c, i.e. it is defined by a linear formula.
Example A. The sequence of odd numbers
a1=3D 1, a2=3D 3, a3=3D 5, a4=3D 7, R= 30;
is an arithmetic sequence because an =3D 2n – 1.
Fact: If a1, a= 2 , a3 , …is an arithmetic seque= nce and that
an =3D d*n + c  then the difference between any t= wo terms is d, &= #13;
i.e. ak+1 – ak =3D= d.
Arithmetic Seque= nces <= /div>
Theorem: If a1, a2 , a3 , …an is a sequence such that
an+1 – an =3D= d for all n, then a= 1, a2, a3,&#= 8230; is  an arithmetic sequence
The following theorem gives the converse of the above fact
and the main formula for arithm= etic sequences. 
In example A, 3 – 1= =3D 5 – 3 =3D 7 – 5 =3D 2 = =3D d.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0195.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
A sequence a1, a2 , a3 , … is an arithmetic sequence
if an =3D= d*n + c, i.e. it is defined by a linear formula.
Example A. The sequence of odd numbers
a1=3D 1, a2=3D 3, a3=3D 5, a4=3D 7, R= 30;
is an arithmetic sequence because an =3D 2n – 1.
Fact: If a1, a= 2 , a3 , …is an arithmetic seque= nce and that
an =3D d*n + c  then the difference between any t= wo terms is d, &= #13;
i.e. ak+1 – ak =3D= d.
Arithmetic Seque= nces <= /div>
Theorem: If a1, a2 , a3 , …an is a sequence such that
an+1 – an =3D= d for all n, then a= 1, a2, a3,&#= 8230; is  an arithmetic sequence and the formula = for the sequence is
an =3D d(n – 1) + a1. <= /span>
The following theorem gives the converse of the above fact
and the main formula for arithm= etic sequences. 
In example A, 3 – 1= =3D 5 – 3 =3D 7 – 5 =3D 2 = =3D d.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0196.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
A sequence a1, a2 , a3 , … is an arithmetic sequence
if an =3D= d*n + c, i.e. it is defined by a linear formula.
Example A. The sequence of odd numbers
a1=3D 1, a2=3D 3, a3=3D 5, a4=3D 7, R= 30;
is an arithmetic sequence because an =3D 2n – 1.
Fact: If a1, a= 2 , a3 , …is an arithmetic seque= nce and that
an =3D d*n + c  then the difference between any t= wo terms is d, &= #13;
i.e. ak+1 – ak =3D= d.
Arithmetic Seque= nces <= /div>
Theorem: If a1, a2 , a3 , …an is a sequence such that
an+1 – an =3D= d for all n, then a= 1, a2, a3,&#= 8230; is  an arithmetic sequence and the formula = for the sequence is
an =3D d(n – 1) + a1. T= his is the general formula of arithmetic sequences.
The following theorem gives the converse of the above fact
and the main formula for arithm= etic sequences. 
In example A, 3 – 1= =3D 5 – 3 =3D 7 – 5 =3D 2 = =3D d.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0142.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0143.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0144.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
=
b. Find the (specific) formula represents this sequence.
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0145.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
=
b. Find the (specific) formula represents this sequence.
=
    Plug a1 = =3D 2 and d =3D 3, into the general formula &n= bsp;
    a= n =3D d(n – 1) + a1 
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0146.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
=
b. Find the (specific) formula represents this sequence.
=
    Plug a1 = =3D 2 and d =3D 3, into the general formula &n= bsp;
    a= n =3D d(n – 1) + a1 
    we get    
    an =3D 3(n – 1) + 2
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0147.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
=
b. Find the (specific) formula represents this sequence.
=
    Plug a1 = =3D 2 and d =3D 3, into the general formula &n= bsp;
    a= n =3D d(n – 1) + a1 
    we get    
    an =3D 3(n – 1) + 2
    an =3D 3n – 3 + 2
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0148.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
=
b. Find the (specific) formula represents this sequence.
=
    Plug a1 = =3D 2 and d =3D 3, into the general formula &n= bsp;
    a= n =3D d(n – 1) + a1 
    we get    
    an =3D 3(n – 1) + 2
    an =3D 3n – 3 + 2
    an  =3D 3n R= 11; 1       the specific formula.
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0149.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
=
b. Find the (specific) formula represents this sequence.
=
    Plug a1 = =3D 2 and d =3D 3, into the general formula &n= bsp;
    a= n =3D d(n – 1) + a1 
    we get    
    an =3D 3(n – 1) + 2
    an =3D 3n – 3 + 2
    an  =3D 3n R= 11; 1       the specific formula.
&#= 13;
c. Find a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:red;position:relative;top:.37em;mso-text-raise:-= 25%; mso-fareast-language:ZH-CN'>1000.
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0150.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
=
b. Find the (specific) formula represents this sequence.
=
    Plug a1 = =3D 2 and d =3D 3, into the general formula &n= bsp;
    a= n =3D d(n – 1) + a1 
    we get    
    an =3D 3(n – 1) + 2
    an =3D 3n – 3 + 2
    an  =3D 3n R= 11; 1       the specific formula.
=
c. Find a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:red;position:relative;top:.37em;mso-text-raise:-= 25%; mso-fareast-language:ZH-CN'>1000.
    Set n =3D 1000 in the specific formula,
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0151.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example B. Given = the sequence 2, 5, 8, 11, …
=
a. Verify it is an arithmetic sequence.
=
    It's arithmetic becau= se 5 – 2 =3D 8 – 5 =3D 11 – 8 =3D … =3D 3 =3D d.
=
b. Find the (specific) formula represents this sequence.
=
    Plug a1 = =3D 2 and d =3D 3, into the general formula &n= bsp;
    a= n =3D d(n – 1) + a1 
    we get    
    an =3D 3(n – 1) + 2
    an =3D 3n – 3 + 2
    an  =3D 3n R= 11; 1       the specific formula.
=
c. Find a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:red;position:relative;top:.37em;mso-text-raise:-= 25%; mso-fareast-language:ZH-CN'>1000.
    Set n =3D 1000 in the specific formula, we get
    a1000 =3D 3(1000) – 1= =3D 2999.
Arithmetic Seque= nces <= /div>
Given the description of a arithmetic sequence, we use the general formula to find the specific for= mula for that sequence. 
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0164.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0197.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0198.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D <= /span>–4 in the general formula an =3D d(n – 1) + a1,
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0199.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0200.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Set n = =3D 6 in this formula, we get the 6th term
a6 =3D –4(6 – 1)= + a1 =3D 5
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0201.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Set n = =3D 6 in this formula, we get the 6th term
a6 =3D –4(6 – 1)= + a1 =3D 5
        = ;   –20 + a1 =3D 5
        = ;            a1 =3D 25
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0202.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Set n = =3D 6 in this formula, we get the 6th term
a6 =3D –4(6 – 1)= + a1 =3D 5
        = ;   –20 + a1 =3D 5
        = ;            a1 =3D 25
To find the speci= fic formula , set 25 for a1 in an = =3D –4(n – 1) + a1
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0203.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Set n = =3D 6 in this formula, we get the 6th term
a6 =3D –4(6 – 1)= + a1 =3D 5
        = ;   –20 + a1 =3D 5
        = ;            a1 =3D 25
To find the speci= fic formula , set 25 for a1 in an = =3D –4(n – 1) + a1 <= /span>
an =3D–4(n – 1) + = 25
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0204.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Set n = =3D 6 in this formula, we get the 6th term
a6 =3D –4(6 – 1)= + a1 =3D 5
        = ;   –20 + a1 =3D 5
        = ;            a1 =3D 25
To find the speci= fic formula , set 25 for a1 in an = =3D –4(n – 1) + a1 <= /span>
an =3D–4(n – 1) + = 25
an = =3D –4n + 4 + 25 =
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0205.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Set n = =3D 6 in this formula, we get the 6th term
a6 =3D –4(6 – 1)= + a1 =3D 5
        = ;   –20 + a1 =3D 5
        = ;            a1 =3D 25
To find the speci= fic formula , set 25 for a1 in an = =3D –4(n – 1) + a1 <= /span>
an =3D–4(n – 1) + = 25
an = =3D –4n + 4 + 25<= span style=3D'mso-spacerun:yes'>    
an =3D –4n + 29
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0206.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Set n = =3D 6 in this formula, we get the 6th term
a6 =3D –4(6 – 1)= + a1 =3D 5
        = ;   –20 + a1 =3D 5
        = ;            a1 =3D 25
To find the speci= fic formula , set 25 for a1 in an = =3D –4(n – 1) + a1 <= /span>
an =3D–4(n – 1) + = 25
an = =3D –4n + 4 + 25<= span style=3D'mso-spacerun:yes'>    
an =3D –4n + 29
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
To find a1000, set n =3D 1000 in the above specific formula
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0207.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Arithmetic Seque= nces <= /div>
To use the arithmetic gen= eral formula to find the specific formula, we need the first term a1 and the difference d.
Set d =3D = –4 in the general formula an =3D d(n – 1) + a1, we get
a= n =3D –4(n – 1) + a.
Set n = =3D 6 in this formula, we get the 6th term
a6 =3D –4(6 – 1)= + a1 =3D 5
        = ;   –20 + a1 =3D 5
        = ;            a1 =3D 25
To find the speci= fic formula , set 25 for a1 in an = =3D –4(n – 1) + a1 <= /span>
an =3D–4(n – 1) + = 25
an = =3D –4n + 4 + 25<= span style=3D'mso-spacerun:yes'>    
an =3D –4n + 29
Example C. Given = a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …an arithmetic sequence with
d =3D –4 an= d a6  = =3D 5, find a1, the speci= fic formula and a1000.
To find a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>1000, set n =3D 1000 in the above specific formula
a1000 =3D –4(1000) + 29 =3D –3971
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0178.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example D. Given that a1, a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>2 , a3 , …is= an arithmetic sequence with a3 =3D –3 and a9 = =3D 39, find d, a1 and the specific formula.
Arithmetic Seque= nces <= /div>
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0208.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example D. Given = that a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …is an arithmetic sequence with a3 = =3D –3 and a9 =3D 39, find d, a1 and the specific formula.
Set n =3D = 3 and n =3D = 9 in the gen= eral arithmetic formula
an = =3D d(n – 1) + a1,
Arithmetic Seque= nces <= /div>
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0209.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences
Example D. Given = that a1, a2 , a<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:89%;color:#003300;position:relative;top:.37em;mso-text-rai= se: -25%;mso-fareast-language:ZH-CN'>3 , …is an arithmetic sequence with a3 = =3D –3 and a9 =3D 39, find d, a1 and the specific formula.
Set n =3D = 3 and n =3D = 9 in the gen= eral arithmetic formula
an = =3D d(n – 1) + a1, we get &#= 13;
a3 =3D d(3 – 1)= + a1 =3D –3 
Arithmetic Seque= nces <= /div>
------=_NextPart_01C957DD.1F8C5810 Content-Location: file:///C:/30889913/3ArithmeticSequences_files/slide0210.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sequences