Question

The 4th and 8th terms of a G.p are 24 and 8/27 respectively. Find the two possible values of a and r

Answer 1

a r^(n-1)
a r^3 = 24
a r^7 = 8/27
r^4 = 8 / (27*24) = 8 /(9*3 *8*3) = (2*2*2) / (3*3*3*3 *2*2*2) = 1/3^4
r = +/- 1/3
I think you can take it from there.

Answer 2

r^4 = (8/27) / 24 = 1/81
r = ±1/3
so ar^3 = 24
a = 24(±27) = ±648