Question

For a geometric series, S4/S8= 1/17, determine the first three terms of the series.

Answer 1

Sn = a(1-r^n)/(1-r), so

(1-r^4)/(1-r^8) = 1/17
r^4 = 1 or 16
1 is no good, so r=2

this will hold, regardless of the first term, T1. Letting T1=1, we have

1,2,4,8,16,32,64,128...
S4 = 15
S8 = 255
S4/S8 = 1/17

Answer 2

why (1-r^4)/(1-r^8)=1/17 then I can get r^4=1or6