Find the 9th Term 5 , 15 , 45 , 135 , 405 , 1215 , 3645 , 10935

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 ${\displaystyle a_1=5}$ and ${\displaystyle r=3}$.

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

Subtract ${\displaystyle 1}$ from ${\displaystyle 9}$.

Raise ${\displaystyle 3}$ to the power of ${\displaystyle 8}$.