# Double sequences with GCD

Given a sequence called $$A$$ including $$50$$ terms ( from $$1$$ to $$50$$), which can be described as ${ A }_{ n }=20+{ n }^{ 2 }$

Given another sequence called $$B$$ including $$49$$ terms, which have a property that ${ B }_{ n }=GCD({ A }_{ n },{ A }_{ n+1 })$

Given that the largest term in $$B$$ is $${B}_{x}$$. Find the value of $$\sqrt { { B }_{ x }+x }$$.

Note: $$GCD(a,b)$$ is denoted as the greatest common divisor of $$a$$ and $$b$$.

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