$(3,5)$ on the plane. It goes 10 units in the direction of positive $x$-axis. Then it turns towards right making an angle of 90 degrees with its initial direction and goes ahead 5 units, Now it again takes a right turn and goes ahead 2.5 units. It keeps turning right and travels half the distance traveled in the turn just before it . This goes on without end. Find the final distance of the particle from the origin $(0,0)$?

A particle is on the pointThe answer would come in the form square root of $x$, submit your answer as $x$.

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