Find the remainder when the sum \[75+76+77+78+79+80+81+82\]is divided by 16.
I notice that the sum is an arithmetic series with a common difference of 1. In this case, n = 8, a = 75, and d = 1, so the sum is \[S_8 = \frac{8}{2}(2 \cdot 75 + (8-1) \cdot 1) = 4(150 + 7) = 628.\] To find the remainder when 628 is divided by 16, I can use long division or a calculator. I get 628 = 16 \cdot 39 + 4, so the remainder is 4. 