# Worksheet: Monotonic Sequences

In this worksheet, we will practice determining monotonic sequences.

**Q1: **

Is the sequence increasing, decreasing, or neither?

- A is increasing.
- B is decreasing.
- C is neither increasing nor decreasing.

**Q2: **

The term of a sequence is . If , is ?

- Ayes
- Bno

**Q3: **

Use , , or to complete the following: A sequence with term is constant if for each .

- A
- B
- C

**Q4: **

Use , , or to complete the following: A sequence with term is strictly increasing if for each .

- A
- B
- C

**Q5: **

Is the sequence increasing, decreasing, or neither?

- A is neither increasing nor decreasing.
- B is increasing.
- C is decreasing.

**Q6: **

Is the sequence , where increasing, decreasing, or neither?

- A is neither increasing nor decreasing.
- B is decreasing.
- C is increasing.

**Q7: **

Is the sequence increasing, decreasing, or neither?

- Adecreasing
- Bneither increasing nor decreasing
- Cincreasing

**Q8: **

Is the sequence increasing, decreasing, or neither?

- Aneither increasing nor decreasing
- Bdecreasing
- Cincreasing

**Q9: **

Is the sequence increasing, decreasing or neither?

- Adecreasing
- Bincreasing
- Cneither increasing nor decreasing

**Q10: **

Is the sequence increasing, decreasing, or neither?

- Aneither increasing nor decreasing
- Bincreasing
- Cdecreasing

**Q11: **

The term of a sequence is . If , is ?

- Ano
- Byes

**Q12: **

Is the sequence increasing, decreasing, or neither?

- A is neither increasing nor decreasing.
- B is decreasing.
- C is increasing.

**Q13: **

Use , , or to complete the following: A sequence with term is strictly decreasing if for each .

- A
- B
- C

**Q14: **

A geometric sequence has first term and common ratio . In which of the following cases will the sequence be decreasing?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q15: **

Consider the sequence for .

Is ?

- Ano
- Byes

Is ?

- Ayes
- Bno

Define and by and . Write in simplified form.

- A
- B
- C
- D
- E

Using the above and the quadratic formula, find the smallest integer so that whenever .