Jag längtar efter helgen, för veckan har varit lång.

Because längta normally uses the preposition efter when you say what someone is longing for or looking forward to. It is a common fixed pattern:

• längta efter något = long for / look forward to something
• längta efter någon = long for / miss someone

So Jag längtar efter helgen is the natural way to say it. Using only längtar would usually sound unfinished unless the thing being longed for is already clear from context.

It can be either, depending on context. In everyday Swedish, it is often quite mild and natural.

• Jag längtar efter helgen usually just means I’m really looking forward to the weekend.
• In a different context, it can be stronger: Hon längtar efter sitt hemland = She longs for her homeland.

So here it does not have to sound dramatic.

Because helgen is the definite form: the weekend.

In Swedish, the definite article is often attached to the noun as an ending:

• en helg = a weekend
• helgen = the weekend

Here the speaker means a specific weekend, usually the coming one or the weekend that both speaker and listener understand from context.

For the same reason: veckan means the week, while vecka means a week.

• en vecka = a week
• veckan = the week

In this sentence, the speaker is talking about the current week, so the definite form is natural: veckan har varit lång = the week has been long.

That is just a basic feature of Swedish grammar. Very often, Swedish expresses the with a suffix instead of a separate word.

For example:

• en bok = a book → boken = the book
• en vecka = a week → veckan = the week
• en helg = a weekend → helgen = the weekend

English uses a separate word (the), but Swedish often adds an ending instead.

Har varit is the present perfect, and it connects the past to the present moment.

• veckan är lång = the week is long
• veckan var lång = the week was long
• veckan har varit lång = the week has been long

Here, the idea is that the week has felt long up to now, and that is why the speaker is looking forward to the weekend. So the present perfect fits very well.

Because lång is the correct form of the adjective for a singular en-word noun used after vara.

vecka is an en-word, and veckan is singular, so the predicate adjective is:

• Veckan är lång.

Compare:

• ett år är långt = a year is long
• dagarna är långa = the days are long

So:

• singular en-word → lång
• singular ett-word → långt
• plural → långa

Here för means because or for.

So the sentence structure is:

• Jag längtar efter helgen = I’m looking forward to the weekend
• för veckan har varit lång = because the week has been long

This för is a conjunction that links two clauses. It is common in both speech and writing, though sometimes eftersom may sound a bit more explicit.

Because för introduces a new main clause, so the clause keeps normal main-clause word order:

• veckan = subject
• har varit = verb

So:

• ..., för veckan har varit lång.

This is normal subject + verb order. Swedish inversion happens in main clauses when something else comes first, for example:

• Nu har veckan varit lång.

But after för, you are simply starting another clause, so veckan har varit is correct.

The safest and most standard choice with längta is längta efter.

• Jag längtar efter helgen = I’m looking forward to the weekend

Till helgen is usually a time expression meaning something like for the weekend or by the weekend:

• Vi åker bort till helgen. = We’re going away for the weekend.

Some speakers may say längtar till helgen in casual speech, but if you are learning standard Swedish, längtar efter helgen is the form to use.

Not always strictly necessary, but it is perfectly natural and helps readability.

Swedish often uses commas a bit less than English, so you may also see:

• Jag längtar efter helgen för veckan har varit lång.

But with two full clauses, many writers prefer the comma:

• Jag längtar efter helgen, för veckan har varit lång.

So the comma here is correct and helpful, even if not absolutely required in every style.