What is the difference between "for the last few years" and "for the past few years"?

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Honestly,  they are pretty much the same, the context is the same.

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I agree - they are used to mean the same thing and in fact "last few years" is slightly more common in the Google corpus. Some people try to argue that you can't say, "last few years" because "last" should be the end of a sequence (e.g. her last book) ... but in fact these expressions are used interchangeably.