Consider the geometric sequence 125/9, 25/3, 5, 3... What is the eighth term of the sequence expressed in a common fraction?

Just multiply each term by the common ratio of 6/10:

 

125/9, 25/3, 5, 3, 9/5, 27/25, 81/125, 243/625, 729/3125, 263/1879........etc.