Daily Math Challenge - April 13, 2023

In a certain sequence ${\mathit{a}}_{\mathbf{1}}\mathbf{=}\mathbf{19}$, ${\mathit{a}}_{\mathbf{2}}\mathbf{=}\mathbf{99}$ and each subsequent term is the average of all preceding terms. Find the value of ${\mathit{a}}_{\mathbf{1999}}$.

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