Answer:
[tex]-13x-23[/tex]
Step-by-step explanation:
Given sequence: [tex]x-9, -x-11, -3x-13[/tex]
Therefore,
- [tex]a_1=x-9[/tex]
- [tex]a_2=-x-11[/tex]
- [tex]a_3=-3x-13[/tex]
General form of an arithmetic sequence: [tex]a_n=a+(n-1)d[/tex]
(where a is the first term and d is the common difference)
To find the common difference, subtract a term from the next term:
[tex]\begin{aligned}d & =a_2-a_1\\ & =(-x-11)-(x-9)\\ & = -x-11-x+9\\ & = -2x-2\end{aligned}[/tex]
Therefore,
[tex]a_n & =(x-9)+(n-1)(-2x-2)[/tex]
To find the 6th term, input n = 6 into the equation:
[tex]\begin{aligned}\implies a_6 & =(x-9)+(6-1)(-2x-2)\\ & = (x-9)+7(-2x-2)\\ & = x-9-14x-14\\ & = -13x-23\end{aligned}[/tex]
