Think A Little Bit

Geometry Level 4

Let \(\forall n \in \mathbb{N}\), \(z_{n+1}=4z_n(1-z_n)\) where \(z_1=\frac{3-\sqrt{5}}{8}\).

Find \(z_5 \times z_{10}\).

If answer can be expressed in form \(a/b\), where \(a\) and \(b\) are coprime positive integers, find \(a+b \).

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