Find the Next Term 7 , 21 , 63 , 189 , 567

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

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=7}$ and ${\displaystyle r=3}$.

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

Subtract ${\displaystyle 1}$ from ${\displaystyle 6}$.

Raise ${\displaystyle 3}$ to the power of ${\displaystyle 5}$.