Sequence Of Cube Roots

Calculus Level 3

A sequence adheres to the recursion relation \(a_{n}=\sqrt[3]{a_{n-1}a_{n-2}a_{n-3}}\) with initial terms \(a_{0}=1,a_{1}=2,a_{2}=1\).

As \(n\) tends to infinity, what is the limit of \( a_n\) correct to 2 decimal places?

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