A geometric sequence is characterized by its common ratio. The formula to calculate the nth term of the given sequence is: [tex]-\frac{8}{3}\times (-3)^n[/tex]
The given parameters are:
[tex]r = -3[/tex] --- the common ratio
[tex]a =8[/tex] --- the first term
The nth term of a geometric sequence is:
[tex]T_n=ar^{n-1}[/tex]
So, we have:
[tex]T_n=8 \times (-3)^{n-1}[/tex]
Apply law of indices
[tex]T_n=8 \times \frac{-3^n}{-3}[/tex]
Rewrite as:
[tex]T_n=\frac{8}{-3}\times (-3)^n[/tex]
[tex]T_n=-\frac{8}{3} \times (-3)^n[/tex]
So, the nth term of the series is: [tex]-\frac{8}{3} \times (-3)^n[/tex]
Read more about geometric sequence at:
https://brainly.com/question/14320920
