Calculation of $\frac{a_{20}}{a_{20}+b_{20}}$? The solution of $\frac{a_{20}}{a_{20}+b_{20}}$ is $-39$ (This is wrote by answer sheet) from the recursive system of equations :
\begin{cases}
a_{n+1}=-2a_n-4b_n  \\
b_{n+1}=4a_n+6b_n\\
a_0=1,b_0=0
\end{cases}
This is taken from $2007$ GATE entrance exam in India.

anyone can show me how we can calculate this answer?

Update 1:

Three answer is added, but my main problem is remains up to yet, non of these three answers didn't include the main aspect of this question. my main problem is via simplification and replacement in last part of solution. 


Hint :
show that
$$\frac{a_{n+1}}{a_{n+1}+b_{n+1}}=-2+\frac{a_{n}}{a_{n}+b_{n}}$$ 
