as stated in my last post - I'm not sure what the problem is?
If you set the shutter speed to 2 seconds that will be more than enough to take a picture of fireworks...
I have an A200 myself, and know if I set it to 'S' on the dial, and move the control wheel infront of the shutter button so that it sets the camera to a 2 second exposure then this is enough to capture the explosion of a firework.
I found that it was relatively straight forward to shoot fireworks using the Shutter Priority Mode.
This is one shot I've achieved with it:
The Exif on this was:
2 Sec exposure
Make sure you have a tripod handy because you wont be able to hold the camera steady for 2 seconds. It's longer than you think it is!
I found 2 seconds to be about the right length of time to have the shutter open to take that burst of light