Question

How do I find the equation of a geometric sequence?

Answer 1

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!