Should "the" and "a" agree in the same sentence?

Example:

She lowered her pen to the blank page and wrote the first verse—followed by a second one.

In this case, I used the first and then a at the end. Is this grammatically correct?


Perfectly correct. Otherwise how would you say:

'I went to THE World Cup in Brazil in AN aeroplane'?

You would either have to say 'a World Cup', or 'the aeroplane', both of which would be nonsense.