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If A(1),A(2),A(3),…,A(n) are n points in...

If `A_(1),A_(2),A_(3),…,A_(n)` are n points in a plane whose coordinates are `(x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)),…,(x_(n),y_(n))` respectively. `A_(1)A_(2)` is bisected in the point `G_(1) : G_(1)A_(3)` is divided at `G_(2)` in the ratio `1 : 2, G_(3)A_(5)` at `G_(4)` in the1 : 4 and so on untill all the points are exhausted. Show that the coordinates of the final point so obtained are `(x_(1)+x_(2)+.....+ x_(n))/(n)` and `(y_(1)+y_(2)+.....+ y_(n))/(n)`

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