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find g12 in the sequence -1,-3,-9,-27,....
a. -59,049
b. -177,147
c. 118,098
d. -19,683

Sagot :

cinderofsoulsss

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]

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