This is a pretty common issue for Trailblazers to have. Here's a link with more information about these GM gauge problems. And where you can purchase replacement parts on Amazon if you want to do the repair yourself.
Trailblazer Speedometer
There is a sender unit in the gas tank something like the ball in a toilet tank.An electric current is sent through this unit and depending on the resistance will register fuel level in the tank. Simply put these wear out,you can't service them and they have to be replaced. Good luck.
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