Question

do the following moves in a coordinate system: start at the origin facing in the positive y direction and move 1 unit. For each subsequent move, it is to turn 90 degrees clockwise and go forward 1 unit farther than it went in the previous move. What is the sum of the coordinates of the robot's position after it moved 14 units in one direction?

Answer 1

take some graph paper and follow the moves:
make a list of
move# -- ordered pair --- sum of coordinates
until you see a pattern

1 -- (0,1) -- 1 ...... up 1 -- add 1 to y
2 -- (2,1) -- 3 ...... right 2 -- add 2 to x
3 -- (2,-3) -- -1 ... down 4 -- add -4 to y
4 -- (-6,-3) -- -9 ... left 8 -- add -8 to x
5 -- (-6,13) -- 7 ... up 16 -- add 16 to y
6 -- (26,13) -- 39 ..right 32 -- add 32 to x
...
..

what do you think?