That depends on whether the person pronounces it as an alphabetism or as a word. Some people say FAQ and pronounce each letter (like /ɛf e kyu/¹), in which case they use "an". If they pronounce it more like a word (like /fæk/) then they'd use "a". So, it's a difference that depends on how the person speaks, and may be right or wrong depending on how each person learns to pronounce the acronym.[1]: My IPA is rusty, so bear with me.
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