Answer:
[tex]a_n[/tex] =[tex]\frac{1}{3}[/tex] [tex]a_n_-_1[/tex] ; [tex]a_1[/tex] =27 is the correct equation
Step-by-step explanation:
For the sequence : 27,9,3,1,1/3, ....
Lets check all the given equations:
-> [tex]a_n[/tex] = -3[tex]a_n_-_1[/tex] ; [tex]a_1[/tex] =27
[tex]a_2[/tex] = -3([tex]a_1[/tex] )= -3(27)=> -81 (this equation doesn't satisfy the sequence)
->[tex]a_n[/tex] =[tex]\frac{1}{3}[/tex] [tex]a_n_-_1[/tex] ; [tex]a_1[/tex] =27
[tex]a_2[/tex] =[tex]\frac{1}{3}[/tex][tex]a_1[/tex] = [tex]\frac{1}{3}[/tex] (27) => 9
[tex]a_3[/tex] =[tex]\frac{1}{3}[/tex][tex]a_2[/tex] = [tex]\frac{1}{3}[/tex] (9) => 3 (this equation describe the sequence)
->[tex]a_n[/tex] =[tex]a_n_-_1[/tex] -3; [tex]a_1[/tex] =27
[tex]a_2[/tex] =[tex]a_1[/tex] -3 = 27-3 => 24 (this equation doesn't satisfy the sequence)
-> [tex]a_n[/tex] =3[tex]a_n_-_1[/tex] - [tex]\frac{1}{3}[/tex] ; [tex]a_1[/tex] =27
[tex]a_2[/tex] =3[tex]a_1[/tex] - [tex]\frac{1}{3}[/tex] = 3(27)- [tex]\frac{1}{3}[/tex] => 80.6 (this equation doesn't satisfy the sequence)
