# Rise and Fall

Calculus Level 4

Suppose $$a > b > 0$$ and $$a_1 =\dfrac{a+b}{2}$$, $$b_1= \sqrt{ab}$$. And for $$n \ge 2$$, $$a_n$$ and $$b_n$$ are defined as $$\large a_n = \frac{1}{2}(a_{n-1} +b_{n-1})$$ and $$\large b_n = \sqrt{a_{n-1} b_{n-1}}$$ respectively.

Then choose the right statement for the sequences $$a_n$$ and $$b_n$$.

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