The general term of the sequence \((-1, \frac{2}{3}, -\frac{1}{2}, \frac{2}{5}, \ldots)\) can be represented by the formula \((-1)^n \frac{2}{n + 1}\).

Here's why:
- For \(n = 1\), the formula gives \((-1)^1 \frac{2}{1 + 1} = -1\), which is the first term of the sequence.
- For \(n = 2\), the formula gives \((-1)^2 \frac{2}{2 + 1} = \frac{2}{3}\), which is the second term of the sequence.
- For \(n = 3\), the formula gives \((-1)^3 \frac{2}{3 + 1} = -\frac{1}{2}\), which is the third term of the sequence.
- For \(n = 4\), the formula gives \((-1)^4 \frac{2}{4 + 1} = \frac{2}{5}\), which is the fourth term of the sequence.

So, the correct answer is \((-1)^n \frac{2}{n + 1}\).