I strongly urge you to take the whole prescription. You can be asymptomatic and have the disease return, except this time it will be resistant to the drug.
The Z-pack is an antibiotic. If you discontinue it before the infection is killed, the bacteria may continue to grow and colonize and become resistant to the antibiotic through mutations.
If you do not finish the entire packet of antibiotics, you may still have an infection that is not entirely cured. Also, you can become allergic to a medication if you do not finish the entire amount prescribed.