A freely falling body traveled xm in n

th
second distance travelled in nāˆ’1
th
second is

distance = (1/2) g t^2

at t = n
d= (1/2) g n^2
at t = n+1
d = (1/2) g (n^2 + 2 n + 1)
distance between = (1/2) g (2n+1)
etc