1. He is writing a letter with a pen.

2. He is writing a letter in pen.

3. He is writing a letter with a ball-point pen.
4. He is writing a letter in ball-point pen.

5. He is writing a letter with a fountain pen.
6. He is writing a letter in fountain pen.
[Is each pair grammatical? Why is 'a' not used after the preposition 'in'?]

Each pair is fine and each pair means the same thing.

Yes, each pair is grammatically correct. The reason why 'a' is not used after the preposition 'in' is because the phrase 'in pen' or 'in fountain pen' is functioning as an adverbial phrase, indicating the instrument or tool used to write the letter. In this context, 'pen', 'ball-point pen', and 'fountain pen' are considered specific enough not to require an indefinite article 'a'.

Each pair of sentences is grammatically correct, but they have slightly different meanings. Let's break them down:

1. He is writing a letter with a pen.
2. He is writing a letter in pen.

Both of these sentences convey the same meaning; the person is using a pen to write the letter. However, the structure is slightly different. In the first sentence, "with" is used to indicate the instrument (pen) being used to write the letter. In the second sentence, "in" is used to describe the material or medium (pen) in which the person is writing the letter.

Now let's analyze the other pairs of sentences:

3. He is writing a letter with a ball-point pen.
4. He is writing a letter in ball-point pen.

Both sentences are grammatically correct, but there is a nuance in meaning. In sentence 3, "with" is used to indicate the instrument (ball-point pen) being used to write the letter. In sentence 4, "in" is used to describe the material or medium, but it sounds a bit awkward because "ball-point pen" is a specific type of pen rather than a medium like "pen" in the previous examples.

Similarly, in pairs 5 and 6:

5. He is writing a letter with a fountain pen.
6. He is writing a letter in fountain pen.

Both sentences are grammatically correct, but sentence 5 uses "with" to indicate the instrument (fountain pen) being used, while sentence 6 uses "in" to describe the material or medium.

As for why the article "a" is not used after the preposition "in" in these cases, it is because we are referring to the material or medium (e.g., pen, ball-point pen, fountain pen) in a general sense, rather than a specific instance.