Find the fifth term of a geometric sequence whose fourth term is 32/27 and whose seventh term is 256/729.

Answer 1

fourth term: ar^4
7th term: ar^7
Let common ratio = r
then
7th term / 4th term = ar^7/ar^4 = r³
therefore
r = cube root of r³

Fifth term = fourth term * r

Answer 2

(256/729)/(32/27)
=8/27
cube root of 8/27
r =2/3
4th term * 2/3
answer is 64/81