Identify the Sequence 125 , 25 , 5 ; dots

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 ${\displaystyle \frac{1}{5}}$ 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 ${\displaystyle a_1=125}$ and ${\displaystyle r=\frac{1}{5}}$.

Apply the product rule to ${\displaystyle \frac{1}{5}}$.

One to any power is one.