Moving along circles For each natural number 
$k$. Let 
$C_k$ denote the circle with radius 
$k$ centimetres and centre at origin. On the circle 
$C_k$
 a particle moves 
$k$ centimetres in the counter - clockwise direction. After completing its motion on 
$C_k$ the particle moves to 
$C_{k+1}$
in the radial direction. The motion of the particle continues in this manner. The particle starts at 
$(1,0)$. If the particle crosses the positive direction of the $x$-axis for the first time on the circle 
$C_n$. What is the value of $n$?

Hint. On each circle the point moves along an arc of $1$ radian. Now a complete revolution is $2\pi\approx 6.28$ radians.
