A series whereby each term is generated by multiplying the previous term by the common ratio (r)

un = ar(n-1) (Where a is the first term u1)

eg. 1,2,4,8,16,32 is a geometric progression with a common ratio of 2.

The common ratio can be obtained by taking any two consecutive terms and dividing the second by the first. (ie. u(n+1) / (un) = r ) If the common ratio for any 2 pairs of terms is not the same then the series is not a geometric progression and the common ratio is meaningless/nonexistant. (After all, it is a common ratio... so how could anything work if it wasnt common to all the terms?)