Find the Next Term 4/9 , -4/3 , 4 ,

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 ${\displaystyle -3}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

Geometric Sequence: ${\displaystyle r=-3}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=\frac{4}{9}}$ and ${\displaystyle r=-3}$.

Combine ${\displaystyle \frac{4}{9}}$ and ${\displaystyle {(-3)}^{n-1}}$.

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