How do I find the equation of a geometric sequence?

1 Answer
MrsRudolph221
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!

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