# Not sure, and positive quantities bite me.

Calculus Level 5

Let $$a$$ and $$b$$ are positive quantities such that $$0 < a < b$$. Define the sequences $$(a_i), (b_i)$$ as follows:

• $$a_1 = \frac{a+b}{2}$$ and $$b_1 = \sqrt{a_1 \cdot b}$$
• $$a_{n+1} = \frac{a_n + b_n}{2}$$ and $$b_{n+1} = \sqrt{a_{n+1} \cdot b_n}$$ for all natural number $$n$$

Which of the following is correct?