Résumés are written in a specific style that relies on conciseness and simplified sentence structures. While this style of writing might seem unusual, it is the generally accepted standard. You can write in either first or third person. It is strictly a matter of preference, but you must be consistent. Whichever version you choose, omit the use of pronouns as they are implied. Use the present tense for activities you currently perform, and past tense for all other activities and achievements.