A bang when the furnace starts is usually delayed ignition — gas builds up before lighting — or expanding ductwork. Delayed ignition deserves a technician soon: it stresses the heat exchanger. A bang when the blower stops is almost always duct metal flexing, which is annoying but harmless.
Typical repairs in Washington, DC: burner cleaning/ignition service $150–$400; blower motor $400–$800; heat exchanger issues usually mean replacement ($5,500–$10,000 installed).
Gas smell, soot, a carbon monoxide alarm, or a bang at every ignition cycle — call now. Heat exchanger cracks are the serious end of this symptom.
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Data by Servik — verified local pros from official license records and public sources. Cost figures are typical ranges, not quotes; a pro's written estimate is the real number.