More fun in 2015, Part 15

Algebra Level 2

{an=an1an2bn1bn2bn=bn1an2+an1bn2 \large \begin{cases} {a_n=a_{n-1}a_{n-2}-b_{n-1}b_{n-2} } \\ { b_n=b_{n-1}a_{n-2}+a_{n-1}b_{n-2} } \end{cases}

Two sequences ana_n and bnb_n begin with values a1=b1=a2=b2=1a_1=b_1=a_2=b_2=1 and satisfy the recursive relations above for n>2n>2.

Find b2015a2015\large \frac{b_{2015}}{a_{2015}}.

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