Find the 5th Term 125 , -25 , 5 , -1

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, ${\displaystyle a_n=a_1{r}^{n-1}}$.

Geometric Sequence: ${\displaystyle r=-\frac{1}{5}}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=125}$ and ${\displaystyle r=-\frac{1}{5}}$.

One to any power is one.

Combine ${\displaystyle {(-1)}^{n-1}}$ and ${\displaystyle \frac{1}{5^{n-1}}}$.

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

Substitute in the value of ${\displaystyle n}$ to find the ${\displaystyle n}$th term.