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?

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