Autosomal DNA results are only helpful with a limited number of generations beyond the testee. As an example AncestryDNA’s ThruLines only includes suggested ancestors back through 5th great-grandparents. The reason for the limit is simple: the further back you go the less autosomal DNA you have from a specific ancestor in that generation.
If you’re thinking of getting a relative DNA tested to help with your research and you are using autosomal DNA–which most of the testing companies do–see if there is a relative who is closer to your problem ancestor than you are.
A relative and I are both descended from a man named Rufus D. Stephens. He is my 4th great-grandfather. He is her 5th great-grandfather. That means there’s a chance I have more of his DNA than she does. Of course, given how the passing of DNA works, there’s a very reasonable probability that she has more of his DNA than I do. But the theoretical odds suggest that I have more because I’m one generation closer. The difference in this case is that my line of descent from Rufus comes in several cases from children who were born later in that descendant’s life.
Look around. My own great-grandmother has great-grandchildren and third great-grandchildren who are about seven years apart in age.