Geometric Sequences and Ratios

The video tutorial covers the concept of geometric sequences, starting with a brief recap of arithmetic sequences. It explains the concept of ratios with examples and then defines geometric sequences, illustrating how to identify them. The tutorial also demonstrates how to find the next terms in a geometric sequence and applies this knowledge to solve a real-world problem involving the half-life of radioactive material. The video concludes with a call to action for viewers to engage with the content.

What is the ratio of 20 to 4?

• 6

• 7

• 5

• 4

Which of the following sequences is a geometric sequence?

• 1, 3, 6, 10

• 5, 10, 15, 20

• 3, 6, 9, 12

• 2, 4, 8, 16

What is the common ratio of the sequence 1, 2, 4, 8?

• 2

• 4

• 3

• 1

If a sequence starts with 2 and has a common ratio of 3, what is the fourth term?

• 81

• 18

• 27

• 54

What is the next term in the sequence 320, 160, 80, 40?

• 20

• 30

• 40

• 50

In the sequence 3, 3√3, 9, what is the common ratio?

• 9

• 3√3

• 3

• √3

What is the next term in the sequence 3√2, 12, 24√2?

• 48

• 96√2

• 48√2

• 96

How much radioactive material remains after 3 days if the initial amount is 500 mg and the half-life is 1 day?

• 31.25 mg

• 125 mg

• 250 mg

• 62.5 mg

What is the common ratio used to calculate the decay of radioactive material with a half-life of 1 day?

• 1/3

• 1/4

• 1/2

• 1

After 5 days, how much of the 500 mg radioactive material remains?

• 15.625 mg

• 31.25 mg

• 62.5 mg

• 125 mg