Answer:
D. [tex]a_n =3(-2)^{n-1}[/tex]
Step-by-step explanation:
Let's try each rule with some numbers:
Rule A.[tex]a_n=2(-3)^{n-1}[/tex]
[tex]n=1, a_n=2(-3)^{1-1}=2(-3)^{0}=2(1)=2[/tex]
[tex]n=2, a_n=2(-3)^{2-1}=2(-3)^{1}=2(-3)=-6[/tex]
[tex]n=3, a_n=2(-3)^{3-1}=2(-3)^{2}=2(9)=18[/tex]
Rule B. [tex]a_n =3(2)^{n-1}[/tex]
[tex]n=1, a_n=3(2)^{1-1}=3(2)^{0}=3(1)=3[/tex]
[tex]n=2,a_n=3(2)^{2-1}=3(2)^{1}=3(2)=6[/tex]
[tex]n=3, a_n=3(2)^{3-1}=3(2)^{2}=3(4)=12[/tex]
Rule C.[tex]a_n =3(-2)^n[/tex]
[tex]n=1, a_n=3(-2)^1=3(-2)=-6[/tex]
[tex]n=2,a_n=3(-2)^2=3(4)=12[/tex]
[tex]n=3,a_n=3(-2)^3=3(-8)=-24[/tex]
Rule D. [tex]a_n =3(-2)^{n-1}[/tex]
[tex]n=1, a_n =3(-2)^{1-1}=3(-2)^{0}=3[/tex]
[tex]n=2,a_n =3(-2)^{2-1}=3(-2)^{1}=3(-2)=-6[/tex]
[tex]n=3,a_n =3(-2)^{3-1}=3(-2)^{2}=3(4)=12[/tex]
The only rule that has two consecutive values of the sequence when evaluated and starts with 3 is the rule D, first has a 3 and then a -6. It is the rule that generates the most similar sequence.
