Python 3, 69 64 61 55 bytes

Takes a list of floats as input.

lambda l:sum(o*-~c*(len(l)-c)for c,o in enumerate(l))

My original code (because the above is quite confusing):

lambda l:sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1))

Example:

l=input().split(" ")
print(sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1)))

Try it here!

Python 3, 69 64 61 55 bytes

Takes a list of floats as input.

lambda l:sum(o*-~c*(len(l)-c)for c,o in enumerate(l))

Try it here!

Python 3, 69 64 61 bytes

Takes a list of numbers as input.

lambda l:sum(eval(o)*-~c*(len(l)-c)for c,o in enumerate(l))

My original code (because the above is quite confusing):

lambda l:sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1))

Example:

l=input().split(" ")
print(sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1)))

Try it here!

Python 3, 69 64 61 55 bytes

Takes a list of floats as input.

lambda l:sum(o*-~c*(len(l)-c)for c,o in enumerate(l))

My original code (because the above is quite confusing):

lambda l:sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1))

Example:

l=input().split(" ")
print(sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1)))

Try it here!

Python 3, 69 64 bytes

Takes a list of numbers as input.

lambda l:sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1))

Example:

l=input().split(" ")
print(sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1)))

Try it here!

Python 3, 69 64 61 bytes

Takes a list of numbers as input.

lambda l:sum(eval(o)*-~c*(len(l)-c)for c,o in enumerate(l))

My original code (because the above is quite confusing):

lambda l:sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1))

Example:

l=input().split(" ")
print(sum(float(o)*c*(len(l)+1-c)for c,o in enumerate(l,1)))

Try it here!