find the 10th term of 8/9,_4/3,2

I will assume you have a typo and you meant,

8/9 , -4/3 , 2

notice that r = -3/2

then term(10) = ar^9
= (8/9)(-3/2)^9
= (8/9)(-196883/512)
= - 2187/64