I have made a post regard this particular question but was incorrect in what I was asking. The sequence needs to be written in sigma notation, not as a summation.
The given sequence is: $$x+2x^3+x^3+2x^4+x^5+2x^6+...$$ I can see that the sum will be an alternating series with a $(-1)^n$ term, starting at $n=1$. After asking my professor for help, he gave me the hint that the sum will in fact have two terms added together.
What I was able to deduce from the given sequence is: $$\sum^\infty_{n=1} 2\frac{1+(-1)^n}{2}x^n$$ Is my assumption correct or does my answer require work?