Approximately, once a week, I hear an explosion (similar to an M-80 firecracker) coming from my home's furnace area. I think its my Carrier furnace. The unit is about 30 yrs. Old. When the furnace is told to heat the house (via the thermostat), the furnace fires up, then the fan comes on, and while the fan in working, the furnace fire goes out for aboat 10 seconds then refires. This happens until the set temperature is reached. Is this the way a furnace is supposed to work?

No, that is not normal. It could be a number of things,maybe a gas valve going bad,gas pressure issue or even dirty burners.

Either way, I strongly suggest shutting the furnace down and getting a pro out to take a look or the next explosion you hear could be your house.