Going to in the First Conditional
OP is unsure if "going to" can be used in the First Conditional.
"If the weather is rainy, I am going to read a book at home." The if-clause is in the first conditional, but what about the main clause?
The structure of a first conditional sentence is "if/when + present simple" followed by "will + infinitive".
For example: "If it is sunny tomorrow, we will go to the beach."
In OP's sentence, the main clause uses "going to" instead of "will."
The "going-to" future refers to planned or intended actions in the future.
We can use the future with going to instead of will in the first conditional. Going to implies a more certain future than will.
- If no one comes to my birthday party, I’m going to be really unhappy.
- John is going to buy that house if he has enough money..
The First Conditional is about possible events in the present or the future.
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Going to in the first conditional
If it rains, I am going to read a book." is the First conditional because the "going-to future" is used to talk about a future event.