Geometric Sequences and Progressions

This video tutorial focuses on geometric progressions, explaining how they differ from linear and quadratic sequences. It covers the concept of multiplying by a constant to find the next term in a sequence, provides examples, and guides viewers through solving problems related to geometric sequences. The video also includes exercises for identifying geometric sequences and solving advanced problems, encouraging students to practice and apply their knowledge.

What is the defining characteristic of a geometric progression?

• Multiplying each term by a constant number

• Subtracting a constant number from each term

• Adding a constant number to each term

• Dividing each term by a constant number

In the sequence 4, 8, 16, what is the common ratio?

• 2

• 4

• 8

• 16

Which of the following sequences is geometric?

• 1, 4, 9, 16

• 1, 4, 16, 64

• 10, 20, 30, 40

• 11, 9, 7, 5

If the third term of a geometric sequence is 80 and the fourth term is 20, what is the common ratio?

• 1/2

• 1/4

• 1/3

• 1/5

What is the difference between the first and fifth terms of a geometric sequence if the third term is 80 and the fourth term is 20?

• 1,275

• 1,280

• 1,285

• 1,290

In a geometric sequence, if the first term is 3 and the second term is 6√2, what is the common ratio?

• √2

• 2√2

• 3√2

• 4√2

What is the next term in the sequence 3, 6√2, 24?

• 36√2

• 12√2

• 48√2

• 24√2

If the first three terms of a geometric sequence are 8, x, and 72, what is the value of x?

• 24

• 32

• 40

• 16

In a geometric sequence, if x/8 = 72/x, what is the value of x?

• 18

• 12

• 24

• 30

What is the square root of 576, which is used to find the value of x in a geometric sequence problem?

• 23

• 22

• 24

• 25