Identify the Sequence -2/125 , -2/25 , -2/5 , -2

This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by ${\displaystyle 5}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=-\frac{2}{125}}$ and ${\displaystyle r=5}$.

Combine ${\displaystyle 5^{n-1}}$ and ${\displaystyle \frac{2}{125}}$.