What is the 7th term of the geometric sequence where a1 = -3 and a5 = -768?

Question

anonymous · Answer

Select one:
A. -12,288
B. -3,072
C. 12,288
D. 3,072

anonymous · Answer

$$a_1,a_2,a_3,a_4...$$
$$a_1,a_1r,a_1r^2,a_1r^3...$$
$$a_5=a_1r^4$$ and so 
$$-768=-3\times r^4$$

anonymous · Answer

okie use of the formula ar^n-1 you have a5 as -768 so -768=-3(r)^5-1 divide 768 by 3 and then take 4th root 
put the value of r in the equation and find the final answer

anonymous · Answer

r = the common difference right?

anonymous · Answer

that makes 
$$r^4=\frac{-765}{-3}=256$$

anonymous · Answer

what @Danyboii  said, take the 4th root to get $r$ then compute 
$$-3\times r^6$$

anonymous · Answer

alright, one moment please.

anonymous · Answer

$r$ is not the "common difference" that is for an "arithmetic sequence"
this is a "geometric sequence" so $r$ is the "common ratio"

anonymous · Answer

oh um... guys... you've lost me... how would I find r exactly? Or in other words, how would I find the common ratio? I'll give it a quick google and see if I can't teach myself.

anonymous · Answer

"to find the common ratio, divide the second term by the first term."

anonymous · Answer

yea but not in this case u r not given the second term

anonymous · Answer

Alright, so for this equation the second term is oh....

anonymous · Answer

that is why in this case you have to take the fourth root

anonymous · Answer

Oh ok I'm getting there (thank you both for being patient) So how on earth do I find this "fourth root"?

anonymous · Answer

just use the formula ar^n-1 so for a5 u have n as 5 a is -3 and = to -768 :3

anonymous · Answer

guess it

anonymous · Answer

or use a calculator

anonymous · Answer

lol 4$$\sqrt[4]{256}$$

anonymous · Answer

http://www.wolframalpha.com/input/?i=4th+root+256

anonymous · Answer

ohhhhh god! Thank you guys... (math sucks for me).

12,288

anonymous · Answer

lol :p shouldnt it be in minus?

anonymous · Answer

should be negative

anonymous · Answer

yea since u r multiplying by -3

anonymous · Answer

oh lol oops I seriously got excited.

anonymous · Answer

you were there, you just forgot the $-$sign

anonymous · Answer

Thank you two so much you guys are great and smart and you two should be proud of yourselves for being so helpful and patient! You guys are the Gandhi's of Openstudy.

anonymous · Answer

Lol :p thanks :3 and yea ur welcome ;3

anonymous · Answer

yw