Learn Danish: Han går i gymnasiet og er sytten år. - He goes to upper secondary school and is seventeen.

No, gymnasiet is a false friend for English speakers. In Danish, it refers to upper secondary school or high school, usually for students aged 16 to 19. If you want to talk about a place to work out, you would use fitnesscenter or sportshal.

Why do we say går i gymnasiet instead of using the preposition til?

When talking about attending an educational institution, Danish uses the preposition i. Just like går i skole, saying går i gymnasiet means you are enrolled as a student there, rather than just physically walking toward the building.

Why does the sentence just say er sytten år without the word for old (gammel)?

While you can absolutely say sytten år gammel to mean seventeen years old, Danish speakers very often drop gammel. Stating that someone er sytten år is a perfectly complete and natural way to give an age.

Why doesn't the word år have a plural ending for seventeen years?

År is a one-syllable neuter noun, meaning it takes et in the singular. In Danish, short neuter nouns like this do not change their form in the indefinite plural. So one year is et år, and seventeen years is simply sytten år.