  Given a Sheffer sequence of polynomials, we introduce the notion of an
associated sequence called the cognate sequence. We study the relationship
between the zeros of this pair of associated sequences and show that in case of
an Appell sequence, as well as a more general family of Sheffer sequences, the
zeros of the members of each sequence (for large n) are either real, or lie on
a line $\Re (z)=c$. In addition to finding the zero locus, we also find the
limiting probability distribution function of such sequences.
