Understanding and making geometric sequences is pretty simple once you get the hang of it!

A geometric sequence is a list of numbers where you find each number by multiplying the one before it by a special number called the common ratio.

How to Identify a Geometric Sequence:

1. Check the Ratios:

   • Take any two numbers next to each other in the sequence and divide them.
   • If the result is the same for every pair of numbers, then you have a geometric sequence.

   For example:

   • In the sequence 2, 6, 18, you can check the ratios:
     • $6 ÷ 2 = 3$
     • $18 ÷ 6 = 3$
   • Since both ratios are the same, this means it is a geometric sequence!

How to Generate a Geometric Sequence:

1. Start with a Term:

   • Begin with any number that isn't zero as your first term. Let's call it $a_1$.

2. Choose a Common Ratio ($r$):

   • Pick any number that isn't zero. This will be your common ratio.

3. Use the Formula:

   • You can find the nth term using this formula: $a_n = a_1 \cdot r^{(n-1)}$
   • This means you can create new terms like:
     • $a_2 = a_1 \cdot r$
     • $a_3 = a_1 \cdot r^2$, and so forth.

That’s all there is to it! With some practice, figuring out and making geometric sequences will become super easy!