An ant finds itself trapped in the xy-plane, and its initial position is (1, 0).

Question

An ant finds itself trapped in the xy-plane, and its initial position is (1, 0). Let S, denotethe cirele with radius & centered around the origin. Starting from (1.o,the walks 1 unit counter-clockwise on S1. Then, it walks directly (radially outward) to S2, on which it will walk 2 units counter-clockwise. Then, it will walk directly to S3 and walk 3 units counter clockwise, and so on, with the ant walking k units on Sk. (See the picture.) When the ant crosses the positive x -axis for the first time since it left (1, 0), t is on Sn. What is n?

Explanation / Answer

It will be on S5 as for fourth tern it will reach 3rd quadrant and (0,4) and at S5 it will reach (5,0) so at S6 it will pass the positive x axis for the first time and s6 will be 6/2(2(1)+(6-1)*1)=21

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