Answer:
[tex]a_{n}[/tex] = [tex](-\frac{2}{3}) ^{n-1}[/tex]
Step-by-step explanation:
The sequence has a common ratio between consecutive terms , that is
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{a_{4} }{a_{3} }[/tex] = - [tex]\frac{2}{3}[/tex]
This indicates the sequence is geometric with nth term
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term
Here a₁ = 1 and r = - [tex]\frac{2}{3}[/tex] , then
[tex]a_{n}[/tex] = 1 [tex](-\frac{2}{3}) ^{n-1}[/tex] = [tex](-\frac{2}{3}) ^{n-1}[/tex]
