# 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 divided in the ration of $$1:1$$ at $$G_1$$
• $$G_1 A_3$$ is divided in the ratio of $$1:2$$ at $$G_2$$
• $$G_2 A_4$$ is divided in the ratio of $$1:3$$ at $$G_3$$
• This process continues until
• $$G_{n-1} A_{k_n}$$ is divided in the ratio $$1:n$$ at $$G_n$$

What are the coordiantes of $$G_n$$?

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