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 \(\text{cm}^{2}\).

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.