Identify the Progression 80 , 20 , 5

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

Geometric Sequence: ${\displaystyle r=\frac{1}{4}}$

This is the form of a geometric sequence.

Substitute in the values of ${\displaystyle a_1=80}$ and ${\displaystyle r=\frac{1}{4}}$.

Apply the product rule to ${\displaystyle \frac{1}{4}}$.

One to any power is one.