Answer:
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] × [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
There is a common ratio r between consecutive terms
r = [tex]\frac{384}{512}[/tex] = [tex]\frac{288}{384}[/tex] = [tex]\frac{216}{288}[/tex] = [tex]\frac{3}{4}[/tex] , then recursive formula is
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] × [tex]\frac{3}{4}[/tex] : a₁ = 512
