Answer: [tex]\bold{a_{n+1}=\dfrac{1}{2}a_n}[/tex]
Step-by-step explanation:
Term-to-term rule is also called the recursive rule.
The recursive rule for a geometric sequence is: [tex]a_{n+1}=a_n\cdot r[/tex] where
- [tex]a_n\ \text{is the previous term}[/tex]
- r is the common ratio
The common ratio (r) is the second term divided by the first term (which is the same ratio for each term divided by its previous term)
In the given sequence {64, 32, 16, 8, 4}, [tex]r=\dfrac{32}{64}\quad \rightarrow \quad r=\dfrac{1}{2}[/tex]
So, the recursive rule is: [tex]{a_{n+1}=a_n\cdot \dfrac{1}{2}[/tex]
