How to create a geometric progression from this probability question?

A and B are shooting at a shooting range, but they only have one six-shooter with one cartridge.*So they agreed to take turns randomly spinning the drum and shooting.*A starts. Find the probability that a shot will occur when A has the revolver.

Solution
The shot occurs on the odd numbered attempt (when A has the revolver); on other attempts the shot does not occur. Therefore, the required probability is the sum ⅙ + (⅚)²·⅙ + (⅚) 4 ·⅙ + ... = 6 / 11 .

I am unsure how they generated this sequence...