Given that,
Sn be the distance travel by the block in the interval t = n-1 and t = n.
Then,
Applying second equation of motion,
Then,
s=ut+12at2....(I)
Since u = 0
At t = n-1
Now, put the value of t in equation (I)
s=0+12×a×(n−1)2
s=a(n−1)22
Now, At t = n
Put the value of t in equation (I)
s′=12an2
Now, the difference
Sn=s′−s
Sn=12a(n2−(n−1)2)
Sn=12a(n2−n2−1+2n)
Sn=12a(2n−1)......(II)
Now, put n+1 in place of n in equation (II)
Sn+1=12a(−1+2(n+1))
Sn+1=12a(2n+1)
Now, the ratio of Sn and Sn+1
SnSn+1=2n−12n+1
Hence, the ratio of SnSn+1 is 2n−12n+1.