Question

a small block slides down a smooth inclined plane , starting from rest at time t = 0 .let Sn be the distance  travelled by the block in time interval t = n - 1 to t = n. then the ratio Sn / Sn + 1 is ??

Joshi sir comment

distance travelled in n seconds = 1/2 an2                          (a is the acceleration in the direction of incline) 

distance travelled in n-1 second = 1/2 a(n-1)2

distance travelled in n+1 second = 1/2 a(n+1)2

so according to given condition Sn / Sn+1 =   [1/2 an-  1/2 an2] /  [1/2 a(n+1)2 -  1/2 an2]

now solve       

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