The 3rd and 7th term of a g.p is 3/4 and 4/27. find the 4th term
3rd term is 3/4 or ar^2 = 3/4
7th germ is 4/27, or ar^6 = 4/27
divide them
ar^6/(ar^2) = (4/27) / (3/4)
r^4 = (4/27)(4/3) = 16/81
r = ± 2/3
into ar^2 = 3/4
a(4/9) = 3/4
a = 27/16
if a = 27/16 and r = 2/3
term(4) = ar^3 = 27/16 * 8/27 = 1/2
if a = 27/16 and r = -2/3
term(4) = -1/2