# Fractal Cubes

The image above shows a construction of fractals by joining smaller and smaller cubes to each face of one single cube.

• In the second figure, the 6 new cubes are formed with a side length of $$\dfrac{1}{3}$$ of its previous cube.
• Then from the third figure and so on, the new cubes can only be formed on the 5 faces of the previous cubes with side length $$\dfrac{1}{3}$$ of its previous cube.

This recursion continues indefinitely.

If $$a_{n}$$ is the total surface area of the $$n^\text{th}$$ figure (from the left), what is the value of $$\displaystyle \lim_{n \to \infty} a_{n}$$?

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