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

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

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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##

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