No, 2 different speeds will not be the issue as the faster stick would automatically only be able to go as fast as the slower stick. But it will not work as the sticks are different capacity, and more than likely different models so are not compatible.
The reason RAM is sold in kits is they are guaranteed to work together, sticks from the same maker, same speed, same GB size but from a seperate silicon batch may not work with each other. RAM is best bought as a kit and what you have will not work no matter what you do.
Sorry to bear such bad news,....
Cheers
This is wrong too. Memory modules with different amounts can, and are (All the time), used. You will sometimes lose dual channel operation (Not to be confused with double data rate, wink, wink) but unless the memory is unsupported by the motherboard because of a configuration problem such as too many ranks, speed beyond what is supported (And even that will usually just downclock in order to be compatible) or is simply too different from the existing memory to want to "play nice", there is no reason you can't add a DIMM that is a different amount than the rest of your memory.
In most cases this will result in some form of "flex mode", even on AMD platforms, where your two matched sticks that are installed in the second and fourth DIMM slots (Over from the CPU going towards the edge of the motherboard. So, 4th slot is closest to the edge. A2 and B2 for most boards, DDR4_1 and DDR4_2 for some boards, but always the second and fourth slots) run in dual channel but the oddball DIMM runs in single channel. It is also possible to have two different sized DIMMs in the A2 and B2 slots and have them run ONLY A PORTION of the memory in dual channel.
So for those configurations, something like a 4GB and 8GB DIMM used together in the A2 and B2 slots COULD result in 8GB of memory (4GB from each slot) running in dual channel and another 4GB running in only single channel.
Regardless of dual channel considerations, as long as the memory is similar enough to play nice, it doesn't matter that they are different capacities.
Short version, you MIGHT be able to get that 16GB DIMM to work with your existing memory, and you might not. It really depends on the quality of the motherboard and whether the three DIMMS want to play nice together or not. It also matters whether your chipset supports 16GB DIMMs, at all.