Hello FAUnited7. I'm Ben. How are you?
In fact there has been no 757, 767 and 777 so far in the 100 series. In the 1970's, when Boeing was designing the 757 and 767, they did design a 100 model but it never left the drawing board because no airline showed any interest in it. So they started with the design of the 200 models right away, which were the first models to leave the drawing board and be bought by airline customers. The 767-200 and 757-200 were the first models of the 757/767 family to come out in the early 1980's. The 767 first flew in September of 1981 and the 757 had its maiden flight in February of 1982.
I think that is why there was initially no 100 model for the 777 because they thought that there would be no interest in a 777-100 from airlines, maybe it is now by principle that when Boeing designs a new aircraft, the first series number to be assigned is 200. However, a 777-100 is still under study at Boeing.
Best regards and have a great year 1999!