Is there a way you can input iterations and functions into a Ti-84 graphing calculator because I have some iterations to complete but I'm not exactly sure if its correct and i want to check my work.

I would say yes.

Have you read your TI-84 manual?
Have you tried google? I did, and got

https://www.google.com/search?q=TI-84+calculator+recursive+functions&ie=utf-8&oe=utf-8