Analyzing Arithmetic Sequences and Inequalities

The video tutorial explains how to analyze arithmetic sequences to determine the number of positive, negative, and terms greater than a specific value using inequalities. It covers finding the nth term, setting up inequalities, and solving them to find the number of terms that meet certain conditions.

What is the first step in analyzing an arithmetic sequence?

• Determining the sequence type

• Calculating the nth term

• Finding the common ratio

• Identifying the first term

In an arithmetic sequence, what does a positive term mean?

• Less than zero

• A negative number

• Equal to zero

• Greater than zero

How do you find the common difference in an arithmetic sequence?

• Subtract consecutive terms

• Add the first term to the last term

• Subtract the first term from the last term

• Multiply consecutive terms

What is the nth term formula for the sequence 27, 25, 23, 21?

• n - 29

• -2n + 29

• -n + 29

• 2n + 29

What is the zero term in the sequence 27, 25, 23, 21?

• 29

• 25

• 27

• 21

How do you solve the inequality -2n + 29 > 0?

• Multiply both sides by 2

• Subtract 29 from both sides

• Add 29 to both sides

• Divide both sides by -2

What is the solution to the inequality -2n + 29 > 0?

• n = 14.5

• n = 15

• n > 14.5

• n < 14.5

How many positive terms are in the sequence 27, 25, 23, 21?

• 13

• 14

• 15

• 12

What does a negative term in a sequence mean?

• Greater than zero

• Equal to zero

• A positive number

• Less than zero

What is the nth term formula for the sequence -82, -79, -76, -73?

• -n - 85

• n + 85

• -3n + 85

• 3n - 85