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$A_{1}, A_{2}, A_{3} .......... A_{n}$ are n points whose coordinates are $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3}) ...... (x_{n}, y_{n})$ . $A_{1} A_{2}$ is bisected at $G_{1}$ . $G_{1} A_{3}$ is divided in the ratio 1:2 at $G_{2}$ . $G_{2} A_{4}$ is divided in the ratio 1:3 at $G_{3}$ and so on until all the points are exhausted. Then the coordinates of the final point so obtained is

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$(\frac{\sum x_{^{1}}}{n - 1}, \frac{\sum y_{^{1}}}{n - 1})$

$(\frac{n}{\sum x_{i}}, \frac{n}{\sum y_{i}})$

$(\frac{\sum x_{^{i}}}{\sum i}, \frac{\sum y_{i}}{Σ i})$

$(\frac{\sum x_{^{i}}}{n}, \frac{\sum y_{i}}{n})$

answer is D.

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Detailed Solution

$G_{1} = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$

$G_{2} = (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$

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