Find the 5th Term 40 , -8 , 8/5 , -8/25

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 ${\displaystyle a_1=40}$ 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 ${\displaystyle 40}$ and ${\displaystyle \frac{{(-1)}^{n-1}}{5^{n-1}}}$.

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