Maths Paper 1 Summary

Sequence i. series
Quadratic sequence

E.g. atbtc I ;3 ; 6,10 ; 15

3atb 2 3 4 5

29 I 1 I




Tn=aNtbntC



Arithmetic sequence


Tn=at( n Nd -




T :
term
A :
1st term 7=9
N :
position Tz=atd
D:
common diff ¢2 -71 arts -72 ) T3=at2d



Arithmetic series [ Has + instead of ;]

Sn=n[2at( n -

1) d) or Sn=n (atl )
f
2 2

V




S :
sum of terms 1st term last term

A : -11

N :
position
D: common diff



> i. by
Geometric sequences stacking

"
Tn= a .tn Tz=4 ar
'
-128 i. ar=4 IT =a

-17=128 at 4 all )=4 T2=ar
R :
common ratio =
4=10 ) a=2
,
T3=av2
A : T1 (a -1-0 ) v5 = 32
N :
position r =
2
,


T : General term




Geometric series


Sn=a(rn 1) -
Sn : sumofterms
f- I N :
position / # of terms

A : T1

( r -1-1 ) R :
common ratio

, Sigma :
sum of £ * Watch out for word : TOTAL *


Pirates were
RANTING and SNARING [Geometric]
because they got SAND on their TANDIS [ Arithmetic]

value to sub
r last
>

>


[ Hit 3)
'


Tn
i -
- I 8
•
start to sub
if it doesn't start @ 1 n= last minus first plus I E. £ D= 8-4+1=5
g
> : "

i. 4


* SS3 :
sum subs ,
-11,7273
* Determine if Arithmetic -
Sn =
? [ 2A + (n 1) d)-




•

Geometric 5h =
all -
rn )
I -
r




fraction series
{ £+41T 8Th numerator
}
→
+
separately
:
. ..

workout .




Th denominator




sum to infinity
-

Sum of geometric series tends to infinity S sum too
:




Series N
convergent :O
-

=


↳ + < r< I A :
IT
R :
common ratio
So = a if -
KR41

1- r



Tn=Sn Sn -
-
I E.
g. 13--53-53-1
=
53-52