# Math Help - Geometric sequence

1. ## Geometric sequence

I am stuck on what to do here.. The answer is +- 1/8

Q) Given that the first term of a geometric sequence is 4, and the third is 1, find possible values for the 6th term.

Do you have to bring in logs or something?

Thanks

2. Originally Posted by Danielisew
I am stuck on what to do here.. The answer is +- 1/8

Q) Given that the first term of a geometric sequence is 4, and the third is 1, find possible values for the 6th term.

Do you have to bring in logs or something?

Thanks
$a_n=ar^{n-1}$

so

$a_1=ar^{0} \iff 4=a$

now

$a_3=4r^2 \iff \frac{1}{4}=r^2 \iff \pm \frac{1}{2}=r$

Finally we get

$a_n=4(\pm \frac{1}{2})^{n-1}$

$a_6=4(\pm \frac{1}{2})^5= \pm \frac{1}{8}$