# Monotone Sequence

### Strictly Monotonically Increasing

A sequence is strictly monotonically increasing if each term is greater than the previous one.

**a _{n+1} > a_{n}**

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.

**a _{n+1} ≥ a_{n}**

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.

**a _{n+1} < a_{n}**

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.

**a _{n+1} ≤ a_{n}**

### Constant Sequence

A sequence is constant if all its terms are equal.

**a _{n} = a_{n+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**.