destination douze

introducing iterative sequences
with a calculator and using the 'ans' key to take forward an answer

[e.g. for question 1 with a seed value of 6:
enter 6, then =
then ans x 2 /3 + 4
=
=
=
a lot of times... 52 to be precise]

students put in any number (a 'seed' value)
and then apply a rule repeatedly - with the outcome becoming the new input etc.
until they have a good reason to stop

what happens for these three iterative rules?
what is the limit?
does it matter what the seed value is?

other iterative sequences have the same limit
what (constant) value needs to be added?

can other iterative sequences with this limit be found?
e.g. for a fraction of 3/8?