## Intermediate Algebra (6th Edition)

The numbers $80, 20,$ and $5$ may be the first three terms of a geometric sequence because they have a common ratio of $\dfrac{1}{4}$. We may appear dividing the term by $4$ to get the next term but this is actually equivalent to multiplying $\dfrac{1}{4}$ to the current term to get the next term.
RECALL: A geometric sequence has a common ratio $r$. The common ratio can be found using the formula: $r=\dfrac{a_n}{a_{n-1}}$ where $a_{n-1}$ and $a_n$ are consecutive terms of the sequence $80, 20,$ and $5$ may be the first three terms of a geometric sequence because they have a common ratio of $\frac{1}{4}$. Note that: $\dfrac{20}{40}=\dfrac{1}{4}$ and $\frac{5}{20}=\dfrac{1}{4}$ Therefore, the numbers $80, 20,$ and $5$ may be the first three terms of a geometric sequence. It appears we are dividing $4$ instead of multiplying $4$, but note that dividing $4$ is the same as multiplying $\dfrac{1}{4}$.