The repeating fraction has a denominator of '2' and a numerator of '3^x', where 3^0=1, 3^1=3, 3^2=9, etc. 

So solving "(3^x)/2=300" solves for the closest decimal:

(3^x)/2=300

click here to solve for x

x=5.8227

...so the x=6 is the smallest integer greater than 300, giving:

3^6/2

click here to simplify

729/2

So 729/2 is the smallest term in the sequence.