articles - Is 'the' necessary when a noun is explained in a same sentence?

I know that definite article is used when a noun is already known in the context.

But I'm not sure with the usage of definite article when I described something explicitly but it hasn't been mentioned before.

So here's my example.

'I believe children are used to listening to the type of music that celebrities promote their life styles'

In the sentence, 'the type of music' was not mentioned before, however I described what type of music it is in the sentence. Also it sounds more comfortable with the article.

Is the article used right? or should it be just 'a type of music'?

Thanks for reading my question.