Barium sulfide vs Ba2S2
As orthocresol pointed out, $\ce{Ba_2S_2}$ does not exist as it's own substance. Perhaps you've misread the question and it instead asks for something else? Otherwise it is wrong, or at least not simplified. Your answer is in effect the correct one, although I'm not sure if sulfur and barium would react like that exactly. 

It might in addition generate multiple polysulfides, such as $\ce{BaS_2}$, $\ce{BaS_3}$, following the rule of $\ce{BaS_{$x$}}$. However, I believe your answer is correct in that the initial reaction between barium and sulfur would produce $\ce{BaS}$, while further reactions might add more sulfurs onto it.