I read the answer comments to your post before writing this, I understand the first answer has a link but what you must understand is that 10 tetras is a lot for a tank of your size. 3 is too small so I'd suggest 5. When it comes to schools you'll want to do them in odd numbers. Second, you don't need to wait 30 days to cycle your tank unless you aren't adding any beneficial bacteria. To shortly describe the Nitrogen Cycle to you, the nitrogen cycle happens when you have fish, when you first get a tank it goes through what is called "New Tank Syndrome" during this period of time is when you DON'T want to add fish, the reason being is that beneficial bacteria is needed to start the nitrogen cycle eliminating any toxins such as Ammonia, Nitrites, and Nitrates. How do you do this?? Well you can buy beneficial bacteria to start that process.
Say you just started your tank, set it up put all your decor and then water. Instead of putting fish in that day, you can go to your local pet store and pick up beneficial bacteria, I'd suggest API Stress Zyme, you'd also want to pick up Stress Coat which is a water conditioner. For the rest of your fish keeping hobby you'll want to use both whenever doing water changes, whatever bacteria you take out, you must put it back in. So you'll double the dose on your tanks first setup so say you have a 10 gal you'll want to treat it like a 20 gallon. You usually do both Stress Zyme and Stress Coat for the first 3 days THEN bring a sample to your pet store for testing. If all is good then get the fish.
If your fish is at the bottom it means it's stressed out either by being sick, not enough decorations, water conditions, or bullying. Stress Coat is a water conditioner but it also has aloe vera which puts the fishes natural slime coat back on it's body when it stresses out, eliminating any chance of getting sick.
I'd suggest more decor, more plants, and add some Stress Zyme and Stress Coat to your tank after doing a 10% water change, you'll only need about 10ml of each instead of the 20ml if you were starting a new tank.
Make sure you keep up on changing your carbon every month, you should be doing monthly water changes of 25% or weekly of 10%. Aquaclear is an amazing filter that I've used for years. Make sure you don't wash the sponge in fresh water but instead wash it in the tank water that you pulled out of the tank, it holds beneficial bacteria and if you wash it with fresh water you can shock the tank. The little bacteria ball things in the bag should also never be washed in fresh water.