Given:
Common ratio=-3
11th term=11
To determine the 13th term, we first note the geometric sequence formula:
[tex]a_n=ar^{n-1}[/tex]
where:
a=1st term
n=nth term
Since the 11th term is 11, we can solve the first term by following the process as shown below:
[tex]\begin{gathered} a_{n}=ar^{n-1} \\ a_{11}=a(-3)^{11-1} \\ 11=a(-3)^{10} \\ Simplify \\ a=\frac{11}{59049} \end{gathered}[/tex]
Next, we plug in a=11/59049 when n=13:
[tex]\begin{gathered} a_{n}=ar^{n-1} \\ a_{13}=(\frac{11}{59049})(-3)^{13-1} \\ Calculate \\ a_{13}=99 \end{gathered}[/tex]
Therefore, the answer is: 99
