# The steps to prove whether a given number sequence is a geometric progression

The steps to prove whether a given number sequence is a geometric progression.

Step 1: List down any three consecutive terms. [Example: T1, T2, T3.]
Step 2: Calculate the values of $\frac{{T}_{3}}{{T}_{2}}$  and $\frac{{T}_{2}}{{T}_{1}}$  .
Step 3: If $\frac{{T}_{3}}{{T}_{2}}=\frac{{T}_{2}}{{T}_{1}}=r$  , then the number sequence is a geometric progression.

Step 4: If $\frac{{T}_{3}}{{T}_{2}}\ne \frac{{T}_{2}}{{T}_{1}}$  , then the number sequence is not a geometric progression.