Maybe, you’ve already faced the problem of person-choosing while creating your CV. It’s hard to answer definitely on the question, which person is better to be used: first or third. The best variant: avoiding both of them. When you’re writing a CV it is obvious that you’re talking about yourself, so using personal pronouns just makes your resume looking redundant. Just compare:
I achieved sales growing on 25% and saved 5% of company’s capital corresponding to my waste-decrease plan.
Achieved sales growing on 25% and saved 5% of company’s capital corresponding to own waste-decrease plan.
The first sentence sounds like boasting yourself, when the second is rather sentence of fact and produces professional impression. Also person neglecting helps to focus employer’s attention on actions and achievements that were done. Results play more important role for every company executive, than people who achieved them.
Surfing through several CV writing services that provide a great amount of recommendation in CV writing, it’s hard to find one definite answer, usage of what person is better. Some of them convince CV writers, that 3d person is a proper variant, because 1d concentrates all attention on the candidate and his/her needs, when the aim of a resume is showing your skills suiting company’s needs. Adherents of 1d person usage are of mind, that usage of 3d person sounds like avoiding responsibility of done work, and, not out of place, most of them are UK-citizens.
Looking on this problem from positions of grammar: in most cases it remains unknown what person is mentioned, when you’re writing in telegraphic style: all verbs in English are conjugated identically in first- and third- person singular in the past tense.
Summarizing all mentioned facts, such conclusion could be done: writing a CV in action-oriented language without subject is more appropriated and efficient, that helps to focus attention on the results of work and avoid confirming the obvious. Such writing style is the choice of professional CV writer!
Note: Covering letter goes along with CV writing principles and is always written in first person. That makes it more personal.