Slow blow fuses are used when you are expecting the odd current spike but the average current still needs to be below a certain value to stop components over heating or blowing up.
eg. tungston lights, heating, inductive loads (motors, fridges, fluro lights, hand tools)
Fast blow fuses are used when part of the circuit needs to be protected against any voltage higher than a certain value.
eg. most digital circuitry
You will usually find both types, but it sound like the fuse that blew is on the main power input so I'd guess it would have been a slow blow. I'm not sure whether the TV will draw a heap of current at the start to fire up the tube or not, you could always but in a fast blow and see if it lasts or not.
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