Solution/s:
1. [tex] \textsf{Let us find the common difference } d [/tex]
[tex] -6 -(-9) = 3 [/tex]
[tex] -3 -(-6) = 3 [/tex]
[tex] 0 -(-3) = 3 [/tex]
[tex] 3 - 0 = 3 [/tex]
[tex] \textsf{The common difference is } 3 [/tex]
[tex] \boxed{d = 3} [/tex]
2. [tex]\textsf{Use the general term formula: } a_n = a_1 + (n-1)d [/tex]
[tex] a_1 [/tex] is already given, which is [tex]-9[/tex]
[tex] a_n = a_1 + (n-1)d [/tex]
[tex] a_n = (-9) + (n-1)(3) [/tex]
[tex] a_n = -9 + 3n - 3 [/tex]
[tex] \boxed{a_n = 3n - 12} [/tex]
Answer:
The nth term is represented as [tex] \boxed{a_n = 3n - 12} [/tex]
