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A seven speed can be either a freewheel or a cassette.
To know if you need a cassette you need to measure the chain. When any one foot interval of chain becomes elongated to 12 1/16th inches if needs to be replaced. Use a good steel ruler with all of the slack out of the chain. If a chain is allowed to stretch more than 1/16" per foot the cogs may be worn enough that the new chain will skip on the teeth.
A 7-speed or 8-speed chain will work.