Answer: [tex]\bold{a_1=6,\quad a_n=-3a_{n-1}}[/tex]
Step-by-step explanation:
The recursive rule for a general geometric sequence is: [tex]a_n=a_{n-1}(r)\quad \text{where}\ a_{n-1}\ \text{is the previous term and r is the ratio}[/tex]
Given the sequence {6. -18, 54, -162, ... }, we can see that
- [tex]\text{the first term}\ (a_1)\ \text{is 6}[/tex]
- [tex]\text{the common ratio (r) is:}\ \dfrac{-18}{6}=-3[/tex]
So, the recursive rule is: [tex]a_n=-3a_{n-1}[/tex]
