How do I find the equation of a geometric sequence?

1 Answer
Apr 25, 2015

A geometric sequence is a list of terms that have a common ratio between them. For example, 4, 8, 16, 32, 64, 128, .... has a ratio of 2. For example, 100, 50, 25, 12.5, ... has a ratio of #1/2#. The formula to compute the #nth# term of a geometric sequence is: #a_n=a_1*r^(n-1)#. The variable #r# stands for the ratio, #a_1# stands for the first term in the sequence, and #n# stands for term numbers. (always counting numbers)

Let's say you are given the following list of terms and asked to write the "equation" for it:

#8, 8/3, 8/9, 8/27, ...#

What is the first term? 8
What is the ratio? #1/3#

So, #a_n=8*(1/3)^(n-1)# will generate any term you want!