Choose a sequence of numbers that represent a geometric series. As an example, let's choose 1, 4, 16, 64, 256
Determine the mathematical representation of the geometric series. Look at the series, use trial and error, and find the formula where a number is multiplied by a constant number to get the next number. In our example, the constant number is 4 and the mathematical representation is Rn = 4(Rn - 1) where Rn is the current number we are looking to calculate and Rn - 1 is the previous number in the sequence.
Verify the mathematical representation by testing it. Using the example representation from Step 2, we need to verity that we can reach the second number in sequence, or R(2), which is 4, with the equation. In this case, the number we are looking to calculate, Rn, is the second number in the sequence and Rn - 1 is the first number in the sequence which is 1 or R(1). Therefore, R(2) = 4(Rn - 1) = 4(1) = 4. For the third number in the sequence, R(3), Rn - 1 is 4, therefore R(3) = 4(4) = 16.