Find the Fourth Term -1/7 , 4/7 , -16/7

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 ${\displaystyle -4}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

Geometric Sequence: ${\displaystyle r=-4}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=-\frac{1}{7}}$ and ${\displaystyle r=-4}$.

Combine ${\displaystyle {(-4)}^{n-1}}$ and ${\displaystyle \frac{1}{7}}$.

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