Arithmetic & Geometric Sequences

PI SEQUENCES
5 7 Marks


ARITHEMATIC PROGRESSION AP


477710 13 I I d 13 10 3


25720 5 10 5 I 4 5 10 5


a nth term a n 1 d a First term
n term no

2 Sum TO FIRST n TERMS d common difference

d NEXT PREVIOUS
Sn a L l last term
I
given 1 n anti
If last term no
I
dEl d2 1 i
Sn d i att se
3
za n 1 i
Nowsolve Quadratic

, GEOMETRIC PROGRESSION GP

1 27478716 32 9 42 2


a 3
it at
t
1 nth term a un a First term
n Term no
2 Sunn OF FIRST n TERMS r Common ratio
r Next
Sn a r 1 all rn previous
r I 1 r
r 1 rel
we choose the based
formula
onvalue of r The denominator
must be positive

3 SUM TO INFINITY
ONLY EXISTS IF A PROGRESSION
is CONVERGING
DIVERGING CONVERGING DIVERGING
yr
I 6 I

, I Cr I


So a
1 r


AP GP
d Next Previous r Next
Previous

nth term at th ild nth terms a rn

Sn Sns alt
i

glate r I

Sn Latin id Sn all rn
I r
I Last

So a
t h