Predict the next number in any sequence
antiRunningSums

You should use a pairwise helper to raise abstraction:

def antiRunningSums(lst):
    return [b - a for a, b in pairwise(lst)]


pairwise can easily be found in the itertools documentation.

runningSums

I think that referencing the list while you are building it is overcomplicated, I would use a variable to be incremented:

def runningSums(lst):
    s = 0
    for addend in lst:
        s += addend
        yield s


To obtain a list call list on the result of this function.