To My Classmates

I know most of us are probably on our nerves right now because of the quiz. I don't find this section clear myself and have difficulties on certain problems like finding a correct recursive definition. I found an easier method to find terms and rate when we are given two different terms that are not consecutive. For instance, in pg. 475 Example 3 states the following:
Example 3.
In a geometric sequence, t(3)= 12 and t(6)= 96. Find t(11)
note that we are not given consecutive sequence integers and t(1) is not given as well.
Well, to solve this formula we plug in the values to solve for t(1) and find the rate.
LOOK!
substituting in the formula Tn= T1 * r^(n-1) gives
t(3)= T1 * r^2=12 and t(6)= T1* r^5=96

so T1 = 12/r^2 = 96/r^5

you cross multiply the two answers and are given the following r^3 = 8 and r=2

T(1)= 12/r^2 = 12/4= 3

so t(11)= 3 * 2^(10)

3072

by plugging in those values and cross multiplying we can get the rate and the first term!
I hope this is helpful!