Monotone Sequence
Strictly Monotonically Increasing
A sequence is strictly monotonically increasing if each term is greater than the previous one.
an+1 > an
2, 5, 8, 11, 14, 17,...
5 > 2; 8 > 5; 11 > 8; ...
Monotonically Increasing
A sequence is monotonically increasing if each term is greater than or equal than the previous one.
an+1 ≥ an
2, 2 , 4, 4, 8, 8,...
2 ≥ 2; 4 ≥ 2; 4 ≥ 4; ...
Strictly Monotonically Decreasing
A sequence is strictly monotonically decreasing if each term of the sequence is less than the previous one.
an+1 < an
1, 1/2, 1/3, 1/4, 1/5, 1/6,...
1/2 < 1; 1/3 < 1/2 ; 1/4 < 1/3; ...
Monotonically Decreasing
A sequence is monotonically decreasing if each term of the sequence is less than or equal to the previous one.
an+1 ≤ an
Constant Sequence
A sequence is constant if all its terms are equal.
an = an+1
5, 5, 5, 5, ...
Examples
Study the following sequences and determine the type of sequence.
1 
3, 4/3, 1, 6/7,...
The sequence is decreasing.
The inequality is satisfied for any value of n.
The sequence is strictly monotonically decreasing.
2 
Each term is greater than the last.
The inequality is satisfied for any value of n.
The sequence is strictly monotonically increasing.
