Answer:
[tex]a_n=3(-3)^{n-1}[/tex]
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
where:
- [tex]a_n[/tex] is the nth term
- a is the first term
- r is the common ratio
Given:
- [tex]a_1=3[/tex]
- [tex]a_2=-9[/tex]
To find the common ratio r, divide consecutive terms:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{-9}{3}=-3[/tex]
Therefore, the equation is:
[tex]a_n=3(-3)^{n-1}[/tex]
