Say there is a moving dot on the coordinate plane. It starts on the coordinates of (0,0). On the 1st day it moves to (1,0) the next, (1,4) then (-8,4) then, (-8,-12), then, (17,-12) and so on. Now I have figured out that on day N, it moves $n^2$ spaces towards a paricular direction.
This is what I am trying to get. How do I generalize this into a some sort of formuala. So how can you write the coordinates of the moving dot on day N, using the letter N in a simplified way?