Head for the first time

One way of solving this (impossible without multiple choice) is to substitute in $n=1$ . Then the probability is obviously $\frac{1}{2}$ and the only expression which is equal to this is $2^{-n}$ = $2^{-1}$ = $\frac{1}{2}$

The die is repeatedly thrown until head occurs.

Given by question that head occurs at nth turn

Hence Till and before only tail occurs.

Now it is tried till nth term

P(Tail)= $\dfrac{1}{2}$ = P(Head)

Now 1st chance that head will not occur = 0.5

2nd time it will not occur = 0.5 *0.5

Like this before nth row head will not occur = $(0.5)^{n-1}$

Hence At last when head occurs, P(which is needed to find) = 0.5 x $(0.5)^{n-1}$ = $2^{-n}$