Question

the sum of the first four terms of a geometry series is 15 and the sum of the next 4 terms is 240.determine the positive constant ratio.

Answer 1

terms are
a , ar, ar^2 ...

sum4 = a(r^4 - 1)/(r-1) = 15
sum8 = a(r^8 - 1)/(r-1) = 15 + 240 = 255

divide the 2nd equation by the 1st
(r^8-1)/(r^4 - 1) = 255/15 = 17
r^4+1)(r^4-1)/(r^4-1) = 17
r^4+1 = 17
r^4 = 16
r^2 = ±4 , and for reals
r = ±2

so the constant ratio is either +2 or -2