Determine whether the following sequences are increasing, decreasing or not monotonic.
A sequence is increasing if each term is less than or equal to the next term.
The sequence is increasing.
A sequence is decreasing if each term is greater than or equal to the next term.
The sequence is decreasing.
This is the graph of a constant sequence which is both increasing and decreasing. Notice that it is not strictly monotonic since each term is equal to the previous and next terms.
The sequence is constant.
A sequence is increasing if each term is less than or equal to the next term. A sequence is decreasing if each term is greater than or equal to the next term. Since neither of these conditions are satisfied here, we conclude that the sequence is not monotonic.
The sequence is not monotonic
This sequence is decreasing since each term is greater than or equal to the next term.
The sequence is decreasing.
A sequence is increasing if each term is less than or equal to the next term. A sequence is decreasing if each term is greater than or equal to the next term. Since neither of these conditions are satisfied here, we conclude that the sequence is not monotonic.
The sequence is not monotonic
The sequence is increasing since each term is less than or equal to the next term.
The sequence is increasing.