Find the remainder of $\frac{3^{11}-1}{2}$ divided by $9$ I have the following question:

Find the remainder of $$\frac{3^{11}-1}{2}$$ divided by $9$

I tried to reformat the question:
$$\frac{3^{11} -1 } {2} \times \frac{1}{9} = \frac{3^{11}-1}{18}$$
Since $3^2 = 9$
$$\frac{3^2(3^9) -1}{3^2 \times2}$$
I don't know where to go next. Anyway, this is one of my many attempts to solve this question, and most of them ends with a complicated solution. I don't want to use modular arithmetic for this question. A hint or anything will help me. 

$$\frac{3^{11}-1}{2}=\frac{3-1}{2}(3^{10}+3^{9}+3^{8}+3^{7}+3^{6}+3^{5}+3^{4}+3^{3}+3^{2}+3+1)\equiv4$$
