is it okay to do this...? and did i get it correct anyway? the third term of an exponential sequence is 12 and the 9th term is 768. find the values of the common ratio.
$$\large ar^2=12 $$$$\large ar^8=768$$
$$\large \frac{ar^8}{ar^2}=\frac{768}{12}$$
$$\large r^6=64 $$
$$\large r=2 \ , \ r=-2$$

I forgot the formulas and decided to go with this but i don't know if it is correct or even if it's acceptable... can anyone confirm for me please?

Question

is it okay to do this...? and did i get it correct anyway? the third term of an exponential sequence is 12 and the 9th term is 768. find the values of the common ratio.
$$\large ar^2=12 $$$$\large ar^8=768$$
$$\large \frac{ar^8}{ar^2}=\frac{768}{12}$$
$$\large r^6=64 $$
$$\large r=2 \ , \ r=-2$$

I forgot the formulas and decided to go with this but i don't know if it is correct or even if it's acceptable... can anyone confirm for me please?

sasogeek · Answer

truth is i've even forgotten if this is exactly how to do it lol. i literally have no memory of the classes i took for this topic

.sam. · Answer

yeah you can do that

parthkohli · Answer

You are perfectly correct, math can be done in infinite ways :)

mimi_x3 · Answer

it looks like a geometric progression.. i dont know what's an exponential sequence.. http://en.wikipedia.org/wiki/Exponential_sheaf_sequence

.sam. · Answer

$$a_3=12$$
$$a_9=768$$
-------------
$$ar^2=12$$
$$ar^8=768$$

$$\frac{12}{r^2}r^8=768$$
$$r^6=64$$
$$r= \pm 2$$

sasogeek · Answer

same thing :) different name

.sam. · Answer

GP formula 

$$\Huge T_n=a_1r^{n-1}$$

sasogeek · Answer

thanks :)

.sam. · Answer

np