Find the number that the sequence converges upon, or approaches. The sequence "1/2, 1/4, 1/8, 1/16..." for example, is approaching 0.
Call the number toward which the sequence converges L. Call x(k) a given number of ordinal k in the sequence, such that x(k+1) is the number that follows. If the absolute value of (x(k+1) - L) divided by the absolute value of (x(k) - L) is equal to a number between 0 and 1, you can say that the sequence converges linearly. We call the result of that equation μ, and μ is the rate of convergence.
Evaluate the other possibilities for μ. If μ is equal to 1, you can say that the sequence converges sublinearly. If μ is 0, the sequence converges superlinearly.
Refer back to the equation in Step 1. For superlinear convergences, you must now determine the exponent on the denominator's expression that will cause μ to be greater than 0. (Note that there was no exponent here in the original equation; or rather the exponent was 1 --- it didn't matter.) Call that exponent q. If q is 2, call your superlinear convergence a quadratic convergence. If q is 3, call it a cubic convergence, and so on.