F5 math problems (Geometric sequence)

the fourth term is 27
let r be the common ratio,
the third term is 27/r
the fifth term is 27r

27/r + 27r = 117/2
6+6r^2 = 13r
6r^2 - 13r + 6 = 0
(2r - 3) (3r - 2) = 0
r = 3/2 or 2/3

when r = 3/2
the geometric sequence is 8, 12, 18, 27, 81/2, ...
when r = 2/3
the geometric sequence is 729/8, 243/4, 81/2, 27, 18, ...