1st+2nd ; EVEN number (0)

1st+3rd ; EVEN number (2)

1st+4th ; EVEN number (4)

1st+5th ; EVEN number (4)

ALL of the original numbers are ODD

or

ALL of the original numbers are EVEN

or

something is wrong wrong with the information.

It's a tad difficult to get an odd number

from the sum of two odd numbers or

from the sum of two even numbers.

Your title is correct.

Fractional numbers do not work.

.