Types and Properties of Arithmetic Progressions

The video tutorial explains three types of arithmetic progressions: increasing, decreasing, and constant. An increasing progression has a positive ratio, exemplified by the sequence 2, 4, 6, 8, 10. A decreasing progression has a negative ratio, shown by the sequence 10, 8, 6, 4. A constant progression has a zero ratio, demonstrated by the sequence 5, 5, 5, 5. The video provides examples and explains the conditions for each type of progression.

What are the three types of arithmetic progressions?

• Ascending, Descending, and Static

• Linear, Quadratic, and Cubic

• Positive, Negative, and Zero

• Increasing, Decreasing, and Constant

In an increasing arithmetic progression, what must be true about the common difference?

• It must be a positive number

• It must be a negative number

• It must be zero

• It can be any number

Which of the following is an example of an increasing arithmetic progression?

• 2, 4, 6, 8, 10

• 1, 1, 1, 1, 1

• 10, 8, 6, 4, 2

• 5, 5, 5, 5, 5

What is the common difference in the decreasing arithmetic progression: 10, 8, 6, 4?

• -1

• 0

• 2

• -2

In a decreasing arithmetic progression, what must be true about the common difference?

• It must be a negative number

• It must be a positive number

• It must be zero

• It can be any number

Which of the following is an example of a constant arithmetic progression?

• 1, 2, 3, 4, 5

• 5, 5, 5, 5, 5

• 2, 4, 6, 8, 10

• 10, 8, 6, 4, 2

What must be the common difference in a constant arithmetic progression?

• Zero

• A positive number

• A negative number

• Any number