What is the sum of the finite arithmethic - 10,-8,-6,-4 ... 24

The answer is 136.

Notice how the numbers go from - 10 to 24 inclusive, skipping at an constant interval of 2. Also notice how - 10 will cancel with 10, - 8 will cancel with 8, etc, all the way down to - 2 cancels with 2. This means you are left with the finite arithmetic sequence 10, 12, 14, 16, 18, 20, 22, 24.

Although adding it up would not be that hard, there is a much simpler way. Add the first term and the last term, divide by 2, then multiply by the number of terms. This gives you your answer, 136.