It is/was/will be the X time.....

[Luis Flmg]

Learn English Vocabulary – The First Time

When you want to talk about your first experience to do something, there are a few ways in English you can do that. The easiest ... Read More…

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• Present tense: This is the first time Jack is working here in the USA.
• Past tense: Today was the first time I ate pizza in New York
• Future tense: Next month is going to be the first time I am going to Peru.

Are these three sentences above correct? I thought they should be:

- This is the first time Jack has worked here in the USA.
- Today was the first time I had eaten pizza in NY.
- Next month will be the first time I will have gone to Peru.

 

[Barque]

This is the first time Jack is working here in the USA.

This is the first time Jack has worked here in the USA.

They don't mean exactly the same thing. The first means he's still working there. The second could be used both if he's working there and if he's recently left the US.

I'd prefer:
This is the first time Jack's worked in the US. (He may either be working there still or may recently have left).
This is/was Jack's first job in the US.

Today was the first time I ate pizza in New York.

This is all right. Your suggested change doesn't sound correct to me.

Next month is going to be the first time I am going to Peru.

Next month will be the first time I will have gone to Peru.

The first is grammatical but is too wordy, and so it sounds stiff. Your revised sentence doesn't sound natural.
I'm going to Peru for the first time next month.
Next month will be my first visit to Peru.
Next month will be the first time I go to Peru.