Given that $A_1,A_2,A_3,A_n$ are $n$ points in a plane whose coordinates are $x_1,y_1),\left(x_2,y_2\right),\left(x_n,y_n\right),$ respectively. $A_1{A}_2$ is bisected at the point $P_1,P_1{A}_3$ is divided in the ratio $A:2$ at $P_2,P_2{A}_4$ is divided in the ratio 1:3 at $P_3,P_3{A}_5$ is divided in the ratio $1:4$ at $P_4$ , and so on until all $n$ points are exhausted. Find the final point so obtained.

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