Closed form of iterated function

Question

It can be easily calculated that performing the operation $(3x+1)$ on a number m, k times yields the result $(3^k)(m)+(3^k -1)/2$

I want to calculate a closed formula for performing the related operation $(3x+1)/2$ on a number m, k times but can't seem to find it.

Thanks for the help

Answer 1

Hints:

1. What is the fixed point of this operation, i.e. for what $x$ do we have $(3x+1)/2 = x$?
2. How does your operation affect displacement from the fixed point?