Recursive sequence (Fibonacci Sequence) & Limits

Hey, I would like some help with this question:

A recursive sequence is a sequence where the th term, , is defined in terms of preceding terms, , etc

one of the most famous recursive sequences is the Fibonacci sequence, created by Leonardo Pisano (1170-1250). The terms of this sequence are define as follows where

It asks me to graph some things, did those, but then it asks me to write an expression, using a limit, to represent the value of the ratios of consecutive terms of the Fibonacci sequence. How would I go about doing this?

Thanks in advance.