Page 25 - Math SL HB Sem 1

GEOME'TRIC SERIES

Consider the sum, S, , of the first n terms of a Gp with first term z, and common ratio r,
i.e
S n: a, + (u,r) + (u,r2; + ... + r,-r)
1zi, (t)
(l)
^r: r Sn- arr (ar2)+ larr;+... +1ar"; (2)
(l)-(2)
_
Sn-rSn - a ar',
(l-r)Sn:a-ar,'

s" "(-l') lo'r"I
lr

a (r'
0r ^ : _-=_ -l\
J n
_1
rl forr> I
NO'IE: r =,s - .s

Example I : Find the sum of the first eight terms of geometric sequence
III II
3'9'27' 8t'243'""

7-13