Step 1 :Given a geometric sequence \(-2, \frac{2}{5}, -\frac{2}{25}, \frac{2}{125} \ldots\)
Step 2 :The first term of the sequence is -2 and the common ratio is -1/5.
Step 3 :The nth term of a geometric sequence can be found using the formula: \(a_{n}=a_{1} \cdot r^{n-1}\) where \(a_{1}\) is the first term, r is the common ratio, and n is the term number.
Step 4 :In this case, \(a_{1}=-2\) and \(r=-1/5\).
Step 5 :Substitute \(a_{1}\) and r into the formula, we get the formula for the nth term of the geometric sequence is \(a_{n}=-2 \cdot\left(-\frac{1}{5}\right)^{n-1}\)
Step 6 :\(\boxed{a_{n}=-2 \cdot\left(-\frac{1}{5}\right)^{n-1}}\) is the final answer.