# An unending sequence of points!

Geometry Level 4

$$A_i$$ (where $$i \in \left\{ 1,2,3,4, \cdots ,n \right\}$$ ) are $$n$$ points in a plane whose coordinates are denoted by $$\left( x_i , y_i \right)$$ respectively.

• $$A_1 A_2$$ is bisected at point $$G_1$$
• $$G_1 A_3$$ is divided in the ratio of $$1:2$$ at $$G_2$$
• $$G_2 A_4$$ is divided in the ratio of $$1:3$$ at $$G_3$$
• $$G_3 A_5$$ is divided in the ratio of $$1:4$$ at $$G_4$$
• $$G_{k-1} A_{k+1}$$ is divided in the ratio $$1:k$$ at $$G_k$$

This goes on until all points are exhausted. What are the coordinates of the final point so obtained?

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