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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