The constant which determines the acceleration (rate of change of gradient / rate of change of rate of change) of a geometric progression. Usually represented by the letter 'r'.
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?)