How do you use the geometric sequence formula to find the nth term?

A geometric sequence is always of the form
#t_n=t_"n-1"*r#

Every next term is #r# times as large as the one before.

So starting with #t_0# (the "start term") we get:
#t_1=r*t_0#
#t_2=r*t_1=r*r*t_0=r^2*t_0#
......
#t_n=r^n*t_0#

Answer:
#t_n=r^n*t_0#
#t_0# being the start term, #r# being the ratio

Extra:
If #r>1# then the sequence is said to be increasing
if #r=1# then all numbers in the sequence are the same
If #r<1# then the sequence is said to be decreasing ,
and a total sum may be calculated for an infinite sequence:
sum #sum=t_0/(1-r)#

Example :
The sequence #1,1/2,1/4,1/8...#
Here the #t_0=1# and the ratio #r=1/2#
Total sum of this infinite sequence:
#sum=t_0/(1-r)=1/(1-1/2)=2#