If your question is whether the proportion of correct answers depends on which sequence they come from, and the order or sequencing is irrelevant let's just call sequence "condition".  The appropriate test here is a chi-square test.  If you have R installed sample code is below.  I've named your conditions A and B.

    dat <- matrix( c(numCorrectA, numWrongA, numCorrectB, numWrongB), ncol = 2 )
    chisq.test(dat)

The component "numCorrectA, numWrongA, numCorrectB, numWrongB" should be replace with the actual number of correct and incorrect items in conditions A and B.  

Please Google chi-square test and read the wikipedia page for requirements, meaning, etc. before using the test indiscriminately.  For example, you should make sure none of the numbers you're entering above is less than 5.  In addition, it's a rather weak statistical evaluation from a theoretical standpoint should the sequences be very long.  Trivial differences in them will come out as passing the test.  Also, the individual samples should be independent.  If they are not then update your questions with more details of what exactly is the design of the study.