Writing and Using Explicit Rules for Geometric Sequences

We want to find the seventh term of the given geometric sequence. First we will find its explicit formula. Let's start by calculating the common ratio.

We will now use the common ratio $\text{-}5$ and the first term $\text{-}1$ to write the formula. $$\begin{array}{c}{a}_n=a_1{r}^{n-1}\iff a_n=\text{-}1\cdot {\left(\text{-}5\right)}^{n-1}\end{array}$$ Finally, to calculate the seventh term we will substitute $7$ for $n$ in our formula.