Geometric Sequences and Common Ratios

This video tutorial covers geometric sequences, focusing on determining the Nth term, common ratio, and sequence formula. It explains the concept of multiplying by a constant to find consecutive terms and how to calculate the common ratio. The video also discusses the domain and range of sequences and provides example problems to illustrate these concepts. Finally, it demonstrates how to determine the formula for a sequence and calculate specific terms.

What is the main goal of the video on geometric sequences?

• To study linear functions

• To explore quadratic equations

• To understand the concept of a common ratio

• To learn about arithmetic sequences

How can you determine the common ratio in a geometric sequence?

• By multiplying consecutive terms

• By adding consecutive terms

• By subtracting consecutive terms

• By dividing a term by the previous term

What is the formula to find any term in a geometric sequence?

• First term multiplied by the common ratio raised to the power of n

• First term plus the common ratio times n

• First term divided by the common ratio raised to the power of n

• First term minus the common ratio times n

In a sequence, what do the values of n represent?

• The common ratio

• The domain

• The range

• The first term

What is the common ratio if the third term is -3 and the second term is 6?

• -2

• 1/2

• 2

• -1/2

If the first term is 3 and the common ratio is 2, what is the fifth term?

• 12

• 24

• 96

• 48

What is the common ratio in a sequence where the first term is 1/3 and the second term is 2/9?

• 1/2

• 1/3

• 2/3

• 3/2

How do you find the sixth term in a geometric sequence?

• Multiply the fifth term by the common ratio

• Subtract the common ratio from the fifth term

• Add the common ratio to the fifth term

• Divide the fifth term by the common ratio

What is the sixth term if the first term is 1/3 and the common ratio is 2/3?

• 64/243

• 32/243

• 64/729

• 32/729

What is the base in the formula for a geometric sequence?

• The sum of terms

• The last term

• The common ratio

• The first term