Why should a distribution being pseudorandom strictly be a sequence of distributions being pseudorandom According to Katz Lindell book,

Let Dist be a distribution on l-bit strings. Informally, Dist is pseudorandom if the experiment in which a string is sampled from Dist is indistinguishable from the experiment in which a uniform string of length l is sampled. (Strictly speaking, since we are in an asymptotic setting we need to speak of the pseudorandomness of a sequence of distributions Dist = {$Dist_{n}$}, where distribution $Dist_{n}$ is used for security parameter n. We ignore this point in our current discussion.) More precisely, it should be infeasible for any polynomial-time algorithm to determine (better than guessing) whether it is given a string sampled according to Dist, or whether it is given a uniform l-bit string.

What do they mean here by sequence of distributions?
A sequence of distributions is a definition of a distribution for each $n$. For example, consider the distribution $Dist_n$ to be a string of length $l(n)$ generated using some pseudorandom generator with a seed of length $n$. Then, for each $n$, the distribution is actually different. The reason why technically you need this is because the notion of negligible is asymptotic - it needs to be a function so that for every polynomial, the function is smaller than it for some large enough $n$.