Hi, I am a sophomore and my freshman year was a lot harder so my GPA was pretty low, but I spent most of my Sophomore trying to improve my GPA and it was moved up to 3.5, but I don't think this would get me into Harvard.
Instead of trying to focus on grades, Harvard also considers other points. This could be community service, job, internships, business, blogs, sports, etc. It is not just about how many things you do or what they are, but how passionate you are about it. Instead of being average at three sports you could excel in one. Hope this helps! Please approve my answer!
Good working raising your GPA! It's a little tricky to know how much you can improve it without knowing what it was initially, how many classes you've taken, and how many more classes you can take. Of course, your best bet to improve your chances at a Harvard acceptance as far as grades are concerned is to ace everything for the rest of high school. It's usually extremely difficult to get into Harvard with anything less than a ~3.8 unweighted, and to be competitive, you generally want to have at least a 3.9. That said, admissions officers are understanding of students who had a rough transition to high school but showed great improvement thereafter. Demonstrating that your grades increased each year (or have been perfect since freshman year), is definitely a good thing.
Whether or not you ultimately get into Harvard, though, I'm sure you'll have many good options down the road!
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I had a 3.1 GPA freshman year then I had a 4.0 last semester, which averaged my high school GPA to a 3.5.