A freely falling body traveled x_n in n^th second distance travelled in n-1^th second is

According to the question we get, 

let the freely falling  body distance moved in n^th  seconds = x_n = $\frac{1}{2}g(2n-1)$

and in (n-1)^th = X_n-1  =   $\frac{1}{2}g\left(2\right(n-1)-1)$

therefore X_n-1 = $\frac{1}{2}g(2n-1)-2) = x-g$.