急 ! F5 sequence #35

(a) The total length of the ant's route is ：
200 + 100 + 50 + ...
= 200 / (1 - 1/2)
= 400 (units)

(b) The position of x-coordinate is :
0 + 100 - 25 + 25/4 - 25/16 + ...
= 100 / [1 - (-1/4)]
= 80
The position of y-coordinate is :
= 0 + 50 - 25/2 + 25/8 - 25/32 + ...
= 50 / [1 - (-1/4)]
= 40
Therefore, the coordinates of the final position of the ant is (80, 40)

a) first term = 200
common ratio = 0.5
the total length = 200 / (1 - 0.5) = 400

b) In direction along y axis from A, first term = 50
common ratio = -0.25
so, the y coordinate of the final position is 50 / (1 - (-0.25)) = 40
In direction along x axis from A, first term = 100
common ratio = -0.25
so, the x coordinate of the final position is 100 / (1 - (-0.25)) = 80

the coordinate of the final position is (80,40).