Grade 12 IEB Sequences and Series Notes

, Sequences +
Series

sequence :
3; 6
; 9 ; 12 . . .




series :
3 + 6 + 9 +
12 . . .




Types of Sequences
1 . Arithmetic (ASIAP)
·




constant difference (d) between consecutive terms



Egi T2y+ 3) Tay
a 1d ; a +
2d + 3d
;
+
; a a



: Tn =
a
+ (n -

)d
-
C


Sum of Terms (Sn)
* Sn =
a ↓ (and) + (a+ 2d) +
. . . . .
+ [a + (n -


1d]
Sn =
[a +
(n - d] +
(a +
(n
-



2)a] (a + + (n -
3)d] . . . . .
+ A

2Sn =
(2a
(n )d] [2a (n 1)d] [2a (n - id]
+ -
+ + - + +
. . . . .




-
n ter ms




2Sn
=
n[2a (n 1)d] + -




Sn
=
E(a +
(n 1)d] -




Consider 7
; 19 ; 21

& Find first ter m
+ constant difference


a =
7 : a =
7



2) Determine Trai


Tio = a +
(n -

1)d

Tio =
7 +
(10 1)7 -




T10 =
70




3) Determine Thi

in =
a + (n 1)d -




Tn
=
7 + (n 1)() -




Tn =
7 +
7n-7

=
Tn Tn




1) Determine So

Sn =
E(2a + (n -


id]
so =
=(2 7 .
+ (0 -


1)7]
S6 =
3(14 +
35)
So 49
=
3
.




S6 =
147