Somewhere in between...

Algebra Level 5

Let \({ a }_{ 1 }>{ a }_{ 2 }>0\) and \({ a }_{ n+1 }=\sqrt { \left( { a }_{ n }{ a }_{ n-1 } \right) } \) ; \(n\ge 2\). If \(\displaystyle{\lim_{ n\rightarrow \infty }{ a }_{ n }}=l{ a }_{ 1 }^{ m }{ a }_{ 2 }^{ n }\), then what is the value of \(l+m+n?\)

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