It's 56. Here's why: The odd numbered terms can be considered to form this arithmetic sequence: 10, 33, 56, 79, 102, 125, 148, 125, ... The even numbered terms form this arithmetic sequence 51, 44, 37, 30, 23, 16, 9, ,2 ... Write them together: 51, 44, 37, 30, 23, 16, 9, ,2 ... 10, 33, 56, 79, 102, 125, 148, 125, ... 10,51,33,44,56,37,79,30,102,23,125,16,148,9,125,2 ... So the next term is 56. There are many other possible answers, but this one is just as correct as any. If your teacher says no, he/she is just plain wrong. Edwin