Sequences & Series
,at
Set of
Sequences
=
numbers written in ORDER
according to some MATH RULE .
Arithmeticsequendicefferent.s.a.E:E?e=n.-
•
General Formula :
¥aa*n . ..
Riga "iiqa;÷
.
NBA
"
Tai Ts T4 Determine the 1st 4 terms
"
.
Te •
Z d atd at2d atsd → Do I know the 1st 4 terms ?
Tz = T ,
t d →
T T !⑤T Tu
Est
.
i - d -
-
Tz - T, a- ; asd ; ; ats
Tn ( 1) d tf first 4 terms are not
given }
NIGH ,yyTn=atdnd
at
'
• =
n -
,
then you must write them out
Tn dnt Ca d ) = -
generally B.
y mute
J
=
Vallee of 'T A
any
train.ie at d) LINEAR EQUATION
Geometricsequence
• Common Ratio = r
Nik .
¥ =
Proportion Laws
Gente,ral Fortman
• :
T, I, T, =
T ,
x r r = T2
⑦ a
; ar ; are ; ar
3
: .
-
-
ar TT
Quadratics Tn = Arn
-
I
atbtc -
- 8; 18:30 ; 44
3atb=tYotYz If +
Tn = an't bntc
Za
¥ ¥ -
-
, Series
=
Sum of the terms of a
sequence
sequence : 2; 4
; ; 8 ; 10 : 612 ; - . .
Series : •
2 t 4 t 6 t 8 t lo t 12 t - - -
•
I 3
-
5 7 9
-
l l -
-
- -
- - -
6 t 12 18+24 30 +36
sum of isptkrm
• - -
-
. . .
• S = T NBA .
, ,
q
Sa Ti Tz Sz Sit Te
Aikfnawtrewagy
= t =
→
Ss Sa t Tz
-
S3 =
T , t Ta t Ts =
S4 = T, t Ta t Ts t Ty S4 = Ss t Ty
•
Sz = S , t Ta Eg . ) Sn = n ( 23 -3N )
i .
Tz = Sa - S . I -
- S ,
23 = -
34 ) =
20
-0
Ta -
- Sz S -
,
2/23-3121 )
20=14-0
= -
Ts =
S3S2 -
=3 (23-361) -
34
=8→
Proofed Bookworm
Arithmetic : a
-
-
T, d Ta -
-
-
T, Tn = at Cn Ild
-
-
-
l
①
Sn a Atd and t th Zd l d l
I
=
t t -
-
- - t -
② tatted tatd
Sn =
l t l d - t l Zd-
t . . .
a
① t ②
i. 25N = ( atl ) t Cath ) t ( ate It - - - t late ) t ( atl)
28in = (atl ) to n times
28N = n ( atl )
Iz ( atl )
: .
Sn =
z[at attn Hd ]
i . Sn -
-
-
Sn
Eknath Hd )
-
-
-
-
,at
Set of
Sequences
=
numbers written in ORDER
according to some MATH RULE .
Arithmeticsequendicefferent.s.a.E:E?e=n.-
•
General Formula :
¥aa*n . ..
Riga "iiqa;÷
.
NBA
"
Tai Ts T4 Determine the 1st 4 terms
"
.
Te •
Z d atd at2d atsd → Do I know the 1st 4 terms ?
Tz = T ,
t d →
T T !⑤T Tu
Est
.
i - d -
-
Tz - T, a- ; asd ; ; ats
Tn ( 1) d tf first 4 terms are not
given }
NIGH ,yyTn=atdnd
at
'
• =
n -
,
then you must write them out
Tn dnt Ca d ) = -
generally B.
y mute
J
=
Vallee of 'T A
any
train.ie at d) LINEAR EQUATION
Geometricsequence
• Common Ratio = r
Nik .
¥ =
Proportion Laws
Gente,ral Fortman
• :
T, I, T, =
T ,
x r r = T2
⑦ a
; ar ; are ; ar
3
: .
-
-
ar TT
Quadratics Tn = Arn
-
I
atbtc -
- 8; 18:30 ; 44
3atb=tYotYz If +
Tn = an't bntc
Za
¥ ¥ -
-
, Series
=
Sum of the terms of a
sequence
sequence : 2; 4
; ; 8 ; 10 : 612 ; - . .
Series : •
2 t 4 t 6 t 8 t lo t 12 t - - -
•
I 3
-
5 7 9
-
l l -
-
- -
- - -
6 t 12 18+24 30 +36
sum of isptkrm
• - -
-
. . .
• S = T NBA .
, ,
q
Sa Ti Tz Sz Sit Te
Aikfnawtrewagy
= t =
→
Ss Sa t Tz
-
S3 =
T , t Ta t Ts =
S4 = T, t Ta t Ts t Ty S4 = Ss t Ty
•
Sz = S , t Ta Eg . ) Sn = n ( 23 -3N )
i .
Tz = Sa - S . I -
- S ,
23 = -
34 ) =
20
-0
Ta -
- Sz S -
,
2/23-3121 )
20=14-0
= -
Ts =
S3S2 -
=3 (23-361) -
34
=8→
Proofed Bookworm
Arithmetic : a
-
-
T, d Ta -
-
-
T, Tn = at Cn Ild
-
-
-
l
①
Sn a Atd and t th Zd l d l
I
=
t t -
-
- - t -
② tatted tatd
Sn =
l t l d - t l Zd-
t . . .
a
① t ②
i. 25N = ( atl ) t Cath ) t ( ate It - - - t late ) t ( atl)
28in = (atl ) to n times
28N = n ( atl )
Iz ( atl )
: .
Sn =
z[at attn Hd ]
i . Sn -
-
-
Sn
Eknath Hd )
-
-
-
-
