What is the sum of all the integers between -12.1 and 3.3?
The smallest integer between -12.1 and 3.3 is -12, and the largest is 3. The formula is S_n = n/2 (a_1 + a_n), where n is the number of terms, a_1 is the first term, and a_n is the last term. In this case, n is the number of integers from -12 to 3, inclusive. I can count them by adding 1 to the difference between the endpoints: n = 3 - (-12) + 1 = 16. Plugging these values into the formula, I get S_16 = 16/2 (-12 + 3) = 8 (-9) = -72. So the sum of all the integers between -12.1 and 3.3 is -72. 