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In this lesson, we will learn how to determine monotonic sequences.

Q1:

Is the sequence π = οΌ β 1 4 ο π π + 6 increasing, decreasing, or neither?

Q2:

The π t h term of a sequence is π π . If π = π π 2 , is π > π π + 1 π ?

Q3:

Use < , = , or > to complete the following: A sequence with π t h term π π is constant if π π π + 1 π for each π β₯ 1 .

Q4:

Use < , = , or > to complete the following: A sequence with π t h term π π is strictly increasing if π π π + 1 π for each π β₯ 1 .

Q5:

Is the sequence π = β 2 3 π + 1 9 π increasing, decreasing, or neither?

Q6:

Is the sequence π = 2 8 οΌ 2 9 2 8 ο π π β 2 3 , where π β₯ 1 increasing, decreasing, or neither?

Q7:

Is the sequence π = 1 1 π + 4 4 π 2 increasing, decreasing, or neither?

Q8:

Is the sequence π = β 9 π β 3 2 π increasing, decreasing, or neither?

Q9:

Is the sequence π = ( β 3 1 ) π π increasing, decreasing or neither?

Q10:

Is the sequence π = 1 1 9 π β 1 6 π increasing, decreasing, or neither?

Q11:

The π t h term of a sequence is π π . If π = π π 2 , is π > π π π + 1 ?

Q12:

Is the sequence π = β 1 1 + 2 π π increasing, decreasing, or neither?

Q13:

Use < , = , or > to complete the following: A sequence with π t h term π π is strictly decreasing if π π π + 1 π for each π β₯ 1 .

Q14:

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

Q15:

Consider the sequence for .

Is ?

Define and by and . Write in simplified form.

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

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