The third term of a GP is 9 and the fifth term is 16 find the fourth term, first term and the common ratio

Answer 1

given:
ar^2 = 9
ar^4 = 16
divide the second by the first:
r^2 = 16/9
r = ± 4/3 <---- common ratio

ar^2 = 9
(16/9)a = 9
a = 81/16 <---- first term

check: if r = +4/3
terms would be 81/16, 27/4, 9, 12, 16, ..
if r + -4/3
terms would be 81/16, -27/4, 9, -12. 16

all looks good