Translation:We are sitting at home and watching an American series.
But "series" is also commonly said, and "sarja" MEANS "series", not "show". "We are watching an American TV show" wouldn't really be an accurate translation. It could mean a one-time show, whereas calling it a "sarja"/"series" indicates that it has several parts and you're watching more than one of them (maybe right now you're watching just one, but you probably watch them regularly, or at least, maybe you're watching it for the first time with the idea that if you like it, you'll watch more). It's not a stand-alone TV show, it's a series. They aren't the same.
I know, that's what I used to think. I kept saying "series" in English for years. We have the same word in Czech - "seriál" that we use exclusively for multi-part TV shows, just like the Finnish "sarja". But every American I talked to (and I like talking about TV shows/series a lot) always said "show" even when they heard me use "series". So I was gradually forced to change my mind.
Interesting. I'm American and a native English speaker, and I use both. More specifically, I sometimes say "show" or "TV show" - which could be a one-time thing or an episode of a series or the series itself - and I sometimes say "series" or "TV series" If I use either of the latter two, it makes it clear I'm talking about a multi-part show, typically one that lasts all season. Because the Finnish version says "sarja" and the point of this Duolingo course is to learn what it means in Finnish, I would use "series" as the translation. Otherwise it can give the impression that "sarja" is the appropriate word for any show, whether multi-part or not, and it really isn't. (And in English this sentence wouldn't have ANYTHING in it to indicate the multi-part meaning, if we did not use the word "series".)
EDIT: literally minutes after writing this, I got a text from a friend recommending that I watch a TV series that she has recently started watching, and she referred to it as a "tv series", too. (She's also American.) It's quite possible that it's regional... in some parts of the US they may be less likely to say "series" than I am, but to me it sounds entirely natural.
The country with the official name of Amerikan Yhdysvallat is usually referred by a short name Yhdysvallat. From that you form an adjective and an inhabitant name yhdysvaltalainen (cf. es estadounidense). These words are almost exclusively used in written texts, i.e. you don't write Amerikka if you mean Yhdysvallat, and I would argue, that most also do the same while speaking.
Some use Amerikka while talking about Yhdysvallat, but for most people it is a vague term, usually covering North America.
Thanks for your response, pieni-chilipalko. Here we get into translating literally and translating meaning. How do you rate your sentence above with the original DL sentence: is it equivalent? We are sitting at home and watching is not a construction I would be inclined to use in (Australian) English.
I'm not sufficiently versed in English to say how natural "sitting at home and watching" is compared to "sitting at home watching". I must take your word for it. It could be that the course creator has been influenced by Swedish, which uses such and-constructions almost exclusively to combine two actions (Vi sitter hemma och tittar på en tv-serie från USA).
Continuing the discussion, this time I tried: -We are sitting at home and watch an American series-. This way I get the -and- in the sentence in a (to me) acceptable manner. DL did not like it. I tried to report it for future consideration, but the -Report- button was not there. Overload?