Answer:
[tex]f(n)=-2\cdot f(n-1)[/tex], where f(1)=3
Step-by-step explanation:
The given sequence is; 3, –6, 12, –24, 48, …
The first term of this sequence is
[tex]f(1)=3[/tex]
There is a common ratio of [tex]r=\frac{-6}{3}=-2[/tex]
We can actually use any other two consecutive terms in the sequence to obtain the common ratio.
The recursive formula is given by:
[tex]f(n)=r\cdot f(n-1)[/tex]
We plug in the common ratio to get:
[tex]f(n)=-2\cdot f(n-1)[/tex], where f(1)=3
