If the convergent sequence \(a_n\) of positive numbers satisfies \[\lim_{n\to \infty} a_{n^2}+a_n^2= 56,\] what is the value of \(\lim_{n\to\infty} a_n\)?

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Consider a sequence \(a_n\). If \(a_n\) converges to \(x,\) is it true that every subsequence of the \(a_n\) has a further subsequence that converges to \(x\)?

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