# 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 $$a+b$$.

×