'A' and 'an' mean 'a (any) one' but 'the' refers to someone or something already known.
Can I have a cake?
Can I have the cake with the cherries?
We use 'a' and 'an' when:
We mean one of many and not a special one.
Can you lend me a pen? - Have you got a car?
When we give a person's occupation.
She's an architect.
In fixed expressions such as:
have a rest make a mistake go for a walk in half an hour a lot of time
Use 'an' when the next word starts with a vowel sound:
an apple an egg an Indian an orange an umbrella an hour
however:
a European a ewe a union a Eurasian a hotel a one-way street
Put 'a' or 'an' in the following: