# Infinite Geometric Progression

Geometry Level 2

A square $$B_1B_2B_3B_4$$ is formed by joining the midpoints of the sides of a square $$A_1A_2A_3A_4$$. A third square $$C_1C_2C_3C_4$$ is made in the same way and the process is continued indefinitely.

If $$A_1A_2 = 10 \text{ cm}$$, find the sum of the areas of all the squares so formed in $$\text{cm}^{2}$$.

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