I think the answer is
$\frac{2}{3}$ or $\frac{1}{6}$
Reason
For answer 1: $ $ Each even term is the reciprocal of the preceding odd term. If the fraction is still reducible, then the remainder is the even term. $$$$ $2/3$ is irreducible, so it is the second term. $4/3 = 1 + 1/3$. Thus, $1/3$ is the fourth term. Similarly, $8/3 = 2 + 2/3$. So, the sixth term should be $2/3$ $$$$ For answer 2: Divide the first and second terms, repeatedly by 2 $$$$ So, $3/2,3/4,3/8,3/16\cdots$ - Odd terms $$$$and $2/3,1/3,1/6,1/12,\cdots$ - Even terms