We have two geometric sequences of positive real numbers: $$6,a,b\text{ and }\frac{1}{b},a,54$$Solve for $a$.
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You are a helpful assistant.<|im_end|>
<|im_start|>user
We have two geometric sequences of positive real numbers: $$6,a,b\text{ and }\frac{1}{b},a,54$$Solve for $a$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3\sqrt{2}
We have two geometric sequences of positive real numbers: $$6,a,b\text{ and }\frac{1}{b},a,54$$Solve for $a$.
train