What is the point of the term "monotonic" when analyzing sequences? If my understanding is good, a sequence is monotonic if it increase or decrease. In my homework, I was asked to indicate if some sequences were increasing or decreasing, and also to specify if it was monotonic or not. To me, it seems useless to specify if it is monotonic or not as specifying whether the sequence increase/decrease or not will automatically indicate it. Now my question is, is there something that I misunderstood about monotonic sequences, or specifying it is just useless/was just in the goal of seeing if we properly understand the concept ?

Typically, monotonic means either increasing or decreasing, as you say. The terminology for monotonically increasing is 'isotonic', and for monotically decreasing is 'antitonic'