# 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 .

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