Concept:The phrase "out of the blue" is an idiom that means something happens suddenly and without any warning.
Explanation:The sentence says: "Out of the blue came his letter inviting me to stay with him."
Here, "out of the blue" does not refer to the colour of the envelope or the way the letter was transported.
It describes the speaker's feeling when the letter arrived.
The letter came completely unexpectedly and took the speaker by surprise.
Therefore, the most appropriate interpretation is "came unexpectedly."
Options A, B, and D are wrong because they talk about air, colour, and sea, which are not connected to the idiomatic meaning.
Answer:C. came unexpectedly.