Find the Fourth Term -3/5 , 6/5 , -12/5

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 ${\displaystyle -2}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

Geometric Sequence: ${\displaystyle r=-2}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=-\frac{3}{5}}$ and ${\displaystyle r=-2}$.

Combine ${\displaystyle {(-2)}^{n-1}}$ and ${\displaystyle \frac{3}{5}}$.

Move ${\displaystyle 3}$ to the left of ${\displaystyle {(-2)}^{n-1}}$.

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