An elevator weighing 20000 N is supported by a steel
Cable. What is the tension in the cable when the elevator
Is being accelerated upward at a rate of 3.00 m/s
2

The cable must support the weight of the elevator car plus additional force required to accelerate the car upward. So:

F = W + ma

You will need to calculate the elevator's mass, given the fact that it weighs 20000 N. Post back with your final answer and we'll check it for you.