Let's analyze the series: AGW31, DIV35, GKU39, IMT43, ?.
First, look at the pattern in the letters:
A, D, G, I: These letters are moving forward in steps of 3.
G, I, K, M: These letters are moving forward in steps of 2.
W, V, U, T: These letters are moving backward in steps of 1.
Now, look at the numbers:
31, 35, 39, 43: These numbers are increasing by 4.
Thus, the next term in the series should be:
Letters: M, O, S.
Number: 47.
So, the next term is MOS47.