Answer:
[tex]\frac{8}{81}[/tex]
Step-by-step explanation:
Since the sequence is geometric there is a common ratio r between consecutive terms.
r = [tex]\frac{1}{3}[/tex] ÷ [tex]\frac{1}{2}[/tex]
= [tex]\frac{1}{3}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{2}{3}[/tex]
Multiplying [tex]\frac{4}{27}[/tex] by r gives the next term in the sequence
[tex]\frac{4}{27}[/tex] × [tex]\frac{2}{3}[/tex] = [tex]\frac{8}{81}[/tex]
