Answer:
[tex]\frac{9}{2}[/tex]
Step-by-step explanation:
There is a common ratio r between consecutive terms in the sequence, that is
r = [tex]\frac{-\frac{4}{3} }{\frac{8}{9} }[/tex] = [tex]\frac{2}{-\frac{4}{3} }[/tex] = - [tex]\frac{3}{2}[/tex]
This indicates the sequence is geometric.
To obtain the next term multiply the previous term by r, that is
a₄ = 2× - [tex]\frac{3}{2}[/tex] = - 3
a₅ = - 3 × - [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{2}[/tex]
