Start at 12 create a pattern that multiplies each number by 4

So,

Basically, you're asking us to start a pattern with 12 and multiply it for every subsequent term.
12, 12 * 4, 12 * 4^2, 12 * 4^3, ...
12, 48, 192, 384, ...

So the geometric sequence will look like this:



A geometric sequence is a sequence where the next terms are found by performing multiplication or division.  In this case, we are multiplying by 4.  This is opposed to an arithmetic sequence, where we are adding or subtracting.

To show that this geometric sequence works, let's try to find a few terms.  To find the nth term, you just have to plug in the number of the term into the expression for n.

For instance, find the first term.  This is the resulting expression:


Let's try a few more terms.  The 2nd term:


The 3rd term:


And that's how the geometric sequence works.

Hold on lemme do the work