# Race to end Fibonacci

$\large{S=\left( { F }_{ 2015 }+{ F }_{ 2013 } \right) \left( { F }_{ 2013 }+{ F }_{ 2012 } \right) }$

If $$F_{n}$$ is the $$n^\text{th}$$ Fibonacci term, and $$S$$ can be expressed as $$F_{a}$$, then find the value of $$\dfrac{a+2}{10}$$

×