The Brilliant Followers

Let there be $100$ brilliant members labelled $a_1, a_2, a_3, a_4, a_5,\ldots, a_{99}, a_{100}$ In this group of brilliant members, $a_2$ follows $a_1$ , $a_3$ follows $a_2$ , $\ldots$ $a_n$ follows $a_{n-1}$ , till $a_{100}$ follows $a_{99}$ . Other than this group of members, these members have other followers, denoted by $F$ who themselves have no followers. Now, $a_n$ has $n$ followers. Thus, for $a_1$ , the only follower is $a_2$ , while for $a_2$ , he has two followers: $a_3$ and $1 F$ . This pattern continues till $a_{100}$ .

Now, say $a_1$ makes a post, the total number of possible reshares which can be done by $a_2, a_3, a_4,\ldots a_{99}, a_{100}$ and the $F$ s is given by $x$ . All of the $F$ s will definitely reshare a post made or reshared by the person(s) they follow, and all $a_{2n+1}$ , with $n\in\mathbb{N}$ , will do the same thing. However, for all $a_{2n}$ , with $n\in\mathbb{N}$ , the probability that they will reshare something posted by someone they follow is $\frac12$ . The probability that the number of reshares is $\geq\frac{x}{2}$ is given by $\frac{1}{a}$ . Find the last digit of $a$