Find the Next Term 3 , -15 , 75

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 ${\displaystyle -5}$ gives the next term. In other words, ${\displaystyle a_n=a_1{r}^{n-1}}$.

Geometric Sequence: ${\displaystyle r=-5}$

This is the form of a geometric sequence.

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

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

Subtract ${\displaystyle 1}$ from ${\displaystyle 4}$.

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