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 Strictly Monotonically Decreasing Sequence

3, 4/3, 1, 6/7,...

The sequence is decreasing.

Monotonically Decreasing Sequence

Monotonically Decreasing Sequence

Monotonically Decreasing Sequence

Monotonically Decreasing

Sequence Solution

The inequality is satisfied for any value of n.

The sequence is strictly monotonically decreasing.


2 Strictly Monotonically Increasing Sequence

Increasing Sequence

Each term is greater than the last.

Strictly Monotonically Increasing

Strictly Monotonically Increasing

Increasing Sequence

Monotonically Increasing

Sequence Solution

The inequality is satisfied for any value of n.

The sequence is strictly monotonically increasing.