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
