Question

Find g12 in the sequence -1,-3,-9,-27,....

a. -59,049
b. -177,147
c. 118,098
d. -19,683

Answer 1

b.
`a_(12)=-177147`

Explanation:

This is a geometric sequence:

`a_n=a_1x^(n-1)`

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:

`-3/-1=3\\-9/-3=3\\-27/-9=3`

That's the factor, and we know the first term is -1, so you can write the equation for this sequence:

`a_n=(-1)(3)^(n-1)`

Finally, plug in 12 for n and solve:

`a_(12)=(-1)(3)^(12-1)\\a_(12)=(-1)(3)^(11)\\a_(12)=(-1)177147\\a_(12)=-177147`