A string of pearls

Algebra Level 5

Consider an infinite sequence $$\{a_1,\ldots,a_n,\ldots\}$$ such that $J=a_1\left(1-a_2\right)=a_2\left(1-a_3\right)=\ldots$

If $$\displaystyle J=\frac{3}{20}$$, find the maximum value of $$a_{2014}$$.

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