Each term of the given sequence can be rewritten in the form:
[tex] \frac{-8}{3},\frac{-16}{3},\frac{-32}{3},\frac{-64}{3},\frac{-128}{3} [/tex],...
As we can see each term is the double or the twice of each preceding term. Thus, we can say that: [tex] f(x+1)=2f(x) [/tex]. Because, -16/3 is [tex] 2\times\frac{-8}{3}=\frac{-16}{3} [/tex], so on and so forth.
Where f(x) is the preceding term and f(x+1) is the consequent/next term.
Therefore, the formula that can be used to describe the sequence is [tex] f(x+1)=2f(x) [/tex]. Thus, out of the given options, the last/fourth option is the correct option.
