11x1 t14 05 sum of an arithmetic series (2010)

Sum Of An Arithmetic Series

Sum Of An Arithmetic Series

ldldldadaaSn +−+−++++++= 22

Sum Of An Arithmetic Series

ldldldadaaSn +−+−++++++= 22 adadadldllSn ++++++−+−+= 22

Sum Of An Arithmetic Series

ldldldadaaSn +−+−++++++= 22 adadadldllSn ++++++−+−+= 22

lalalalalalaSn ++++++++++++= 2

Sum Of An Arithmetic Series

ldldldadaaSn +−+−++++++= 22 adadadldllSn ++++++−+−+= 22

lalalalalalaSn ++++++++++++= 2( )lan +=

Sum Of An Arithmetic Series

ldldldadaaSn +−+−++++++= 22 adadadldllSn ++++++−+−+= 22

lalalalalalaSn ++++++++++++= 2( )lan +=

( )lan

Sn +=2 if we know l

Sum Of An Arithmetic Series

ldldldadaaSn +−+−++++++= 22 adadadldllSn ++++++−+−+= 22

lalalalalalaSn ++++++++++++= 2( )lan +=

( )lan

Sn +=2 if we know l

otherwise;

Sum Of An Arithmetic Series

ldldldadaaSn +−+−++++++= 22

( ){ }dnaan

Sn 12

−++=

adadadldllSn ++++++−+−+= 22

lalalalalalaSn ++++++++++++= 2( )lan +=

( )lan

Sn +=2 if we know l

otherwise;

Sum Of An Arithmetic Series

ldldldadaaSn +−+−++++++= 22

( ){ }dnaan

Sn 12

−++=

adadadldllSn ++++++−+−+= 22

lalalalalalaSn ++++++++++++= 2( )lan +=

( )lan

Sn +=2 if we know l

otherwise;

( ){ }dnan

Sn 122

−+=

( ) 66 find ,96 and 3 If .. STaige ==

( ) 66 find ,96 and 3 If .. STaige ==

( )lan

Sn +=2

( ) 66 find ,96 and 3 If .. STaige ==

( )lan

Sn +=2

( )96326

6 +=S

( ) 66 find ,96 and 3 If .. STaige ==

( )lan

Sn +=2

( )96326

6 +=S

297=

( ) 66 find ,96 and 3 If .. STaige ==

( )lan

Sn +=2

( )96326

6 +=S

297=

( ) numberseven 100first theof sum theFind ii

( ) 66 find ,96 and 3 If .. STaige ==

( )lan

Sn +=2

( )96326

6 +=S

297=

( ) numberseven 100first theof sum theFind ii100 and 2,2 === nda

( ) 66 find ,96 and 3 If .. STaige ==

( )lan

Sn +=2

( )96326

6 +=S

297=

( ) numberseven 100first theof sum theFind ii100 and 2,2 === nda

( ){ }dnan

Sn 122

−+=

( ) 66 find ,96 and 3 If .. STaige ==

( )lan

Sn +=2

( )96326

6 +=S

297=

( ) numberseven 100first theof sum theFind ii100 and 2,2 === nda

( ){ }dnan

Sn 122

−+=

( ) ( ){ }29942

100100 +=S

( ) 66 find ,96 and 3 If .. STaige ==

( )lan

Sn +=2

( )96326

6 +=S

297=

( ) numberseven 100first theof sum theFind ii100 and 2,2 === nda

( ){ }dnan

Sn 122

−+=

( ) ( ){ }29942

100100 +=S

10100

20250

=×=

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

{ } 100922

10 =+ da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

{ } 100922

10 =+ da

2092 =+ da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

{ } 100922

10 =+ da

2092 =+ da

255 =S

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

{ } 100922

10 =+ da

2092 =+ da

255 =S

{ } 254225 =+ da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

{ } 100922

10 =+ da

2092 =+ da

255 =S

{ } 254225 =+ da

52 =+ da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

{ } 100922

10 =+ da

2092 =+ da

255 =S

{ } 254225 =+ da

52 =+ da

1042

2092

=+=+

da

da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

105 =d

{ } 100922

10 =+ da

2092 =+ da

255 =S

{ } 254225 =+ da

52 =+ da

1042

2092

=+=+

da

da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

105 =d1 2 =∴= ad

{ } 100922

10 =+ da

2092 =+ da

255 =S

{ } 254225 =+ da

52 =+ da

1042

2092

=+=+

da

da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

105 =d1 2 =∴= ad

( )dnaTn 1−+=

{ } 100922

10 =+ da

2092 =+ da

255 =S

{ } 254225 =+ da

52 =+ da

1042

2092

=+=+

da

da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

105 =d1 2 =∴= ad

( )dnaTn 1−+=( )

12

211

−=−+=

n

n

{ } 100922

10 =+ da

2092 =+ da

255 =S

{ } 254225 =+ da

52 =+ da

1042

2092

=+=+

da

da

( ) term.general theand , Find

25. is numbers 5first theand 100 is numbers 10first theof sum The

da

iii

10010 =S

105 =d1 2 =∴= ad

( )dnaTn 1−+=( )

12

211

−=−+=

n

n

{ } 100922

10 =+ da

2092 =+ da

255 =S

{ } 254225 =+ da

52 =+ da

1042

2092

=+=+

da

da

12 ,2 ,1 −===∴ nTda n

( ) ( )∑=

−10

1

63 n

niv

( ) ( )∑=

−10

1

63 n

niv

10 ,24 ,3 ==−= nla

( ) ( )∑=

−10

1

63 n

niv

10 ,24 ,3 ==−= nla

( )lan

Sn +=2

( ) ( )∑=

−10

1

63 n

niv

10 ,24 ,3 ==−= nla

( )lan

Sn +=2

( )

105

2432

1010

=

+−=S

Exercise 6I; 2ace, 4bd, 5ac, 7c, 8f, 9, 11ac, 13be, 16a17bc, 19, 20a*

( ) ( )∑=

−10

1

63 n

niv

10 ,24 ,3 ==−= nla

( )lan

Sn +=2

( )

105

2432

1010

=

+−=S