Recurring Styles 4 - Limit of an Expression!

Calculus Level 5

$\large{\lim_{n \to \infty} \dfrac{x_n \cdot x_{n+2}}{x_{n+1}^2} = 4}$

Let $(x_n)_{n=1}^{\infty}$ be a sequence such that the above limit satisfies, and where $x_i > 0$ for every $i \geq 1$. Then find the value of $\displaystyle {\lim_{n \to \infty} \sqrt[n^2]{x_n} }$.

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