Definition
Geometric sequence
A number sequence made by multiplying by the same fixed number at every step.
What it means
Walk through the sequence using one repeatable multiply step. The multiplier may make terms grow, shrink, switch signs, or become zero; what matters is that the same multiplier is used each time.
Remember it
Geometric sequence: repeat one multiply step.
Example
2, 6, 18, 54 is geometric because each term is 3 times the term before it. Its common ratio is 3, so the next term is 162.
Watch for
3, 6, 9, 12 is not geometric: it adds 3 each time, but its step-by-step multipliers are not the same.
Common mix-up
Geometric sequences repeat a multiplier; arithmetic sequences repeat an added amount.
Exact meaning
A geometric sequence is a number sequence in which each term is multiplied by one fixed number to make the next term.