Page 25 - Math SL HB Sem 1

CE S

GEOMETRIC SEITIES

Consider the sum, S, , of the first n terms of a Gp with first term z, and common ratio r,

i.e Sn:a, +(2, r) t. 1u,r2).r.... +1r,l,rn-t) (l)

(l).r,
) ) (2)
r Sn- ar + ( ar2 + ( ar3 + . . . + ( ar")
(l) (2) Sn-rSn-a-ar'

(l r)Sn = a_ar"

a(l-r')
4,., - lorr < I
lr

t)r ,n _ o(r"-l) forr> I
r -l

NOTE: f, = S, -5,, ,

Example I : Find the sum of the first eigh t tcrrns of gcometric sequcnce
I ll I I
_) 9'27'8t'243'""

2-t3