There are a few mistakes here, I will try to go over them one by one

Asking for the list

L=[int(x) for x in input("please enter a list:").split()]

This will throw a ValueError when it gets fed a non-numeric type. This will also round any float to int

Problem one can be solve by surrounding it with a while loop and a try-catch block

while True:
    try:
        L=[int(x) for x in input("please enter a list:").split()]
        break
    except ValueError:
        pass

The problem with the int can be easily solved by changing int(x) to float(x)

When using float, beware of the nature of floating point numbers

Checking for arithmetic and geometric

In your solution, i never gets incremented, so this only checks the first two values. Borrowing from @dex-ter's comment you can change this to

def is_arithmetic(l):
    return all((i - j) == (j - k) for i, j, k in zip(l[:-2], l[1:-1], l[2:]))

For an explanation why on how this works, check the background of list splicing and zip

For is_geometric you can easily adapt this solution.

This is also an excellent example where unittests would've made this error clear

assert is_geometric((1,2))
assert is_geometric((1,2, 4))
assert is_geometric((1,2, 4, 8))
assert not is_geometric((1,2, 4, 9))
try:
    is_geometric((1, 2, 'a'))
    raise AssertionError('should throw TypeError')
except TypeError:
    pass

The result

Your result only prints True or False is because that's what you tell your program to do. Your IsArithemeticOrGeometric() has no return statement, so it always returns None, which does not get printed. , so all the output comes from print(Arithemetic(L)) or print(Geometric(L))

A possible solution here would be something like this:

def is_arithmetic_or_geometric(l):
    if is_arithmetic(l):
        return 'arithmetic'
    if is_geometric(l):
        return 'geometric'

print(is_arithmetic_or_geometric(L))