Step 1: Find acceleration a. We use the formula for velocity with uniform acceleration: v=u+at. Here, u=0 (because the body starts from rest), and after n seconds, the velocity is v. So: v=an⟹a=
v
n
Step 2: Find displacement in the nth second (Sn). The formula for how far an object moves during the nth second is: Sn=u+
a
2
(2n−1) Since u=0 : Sn=
a
2
(2n−1) Step 3: Find displacement in the (n−1) th second (Sn−1). Plug ( n−1 ) instead of n into the formula: Sn−1=
a
2
(2(n−1)−1) =
a
2
(2n−3) Step 4: Add the displacements for the nth and (n−1) th seconds. Sn+Sn−1=
a
2
(2n−1)+
a
2
(2n−3) Combine the numbers in the brackets: Sn+Sn−1=
