Answer:
b. [tex]a_{12}=-177147[/tex]
Step-by-step explanation:
This is a geometric sequence:
[tex]a_n=a_1x^{n-1}[/tex]
where n is the index in the sequence and x is the common scale factor.
In the given sequence here, the common factor is 3:
[tex]-3\div-1=3\\-9\div-3=3\\-27\div-9=3[/tex]
That's the factor, and we know the first term is -1, so you can write the equation for this sequence:
[tex]a_n=(-1)(3)^{n-1}[/tex]
Finally, plug in 12 for n and solve:
[tex]a_{12}=(-1)(3)^{12-1}\\a_{12}=(-1)(3)^{11}\\a_{12}=(-1)177147\\a_{12}=-177147[/tex]
