Geometric Sequences and Common Ratios

The video tutorial explains how to find the fifth term in a geometric sequence. It starts by introducing the concept of a geometric sequence and the common ratio. The tutorial then demonstrates how to calculate the common ratio and use it to find the fifth term. The process involves multiplying each term by the common ratio, which is negative four in this case. The tutorial concludes by verifying the calculations and confirming that the fifth term is negative eight.

What is the main goal of the problem presented in the video?

• To find the first term of a sequence

• To determine the common ratio

• To identify the type of sequence

• To calculate the fifth term of a geometric sequence

In a geometric sequence, how is each term related to the previous one?

• By subtracting a constant number

• By dividing by a common ratio

• By adding a constant number

• By multiplying by a common ratio

What is the common ratio in a geometric sequence?

• The factor by which each term is multiplied to get the next

• The product of all terms

• The difference between consecutive terms

• The sum of all terms

How do you determine the common ratio from the first term to the second term in this sequence?

• By adding 4

• By dividing by 4

• By multiplying by -4

• By subtracting 4

What is the result of multiplying the first term by the common ratio?

• 1

• 1/2

• 1/4

• 1/8

What is the next step after finding the common ratio?

• Subtract the common ratio from the first term

• Divide the first term by the common ratio

• Verify the common ratio with subsequent terms

• Add the common ratio to the first term

What is the result of applying the common ratio to the second term?

• Negative one-half

• Positive one-half

• Negative one-fourth

• Positive one-fourth

What is the result of applying the common ratio to the third term?

• Positive four

• Negative four

• Positive two

• Negative two

What is the final step to find the fifth term?

• Add the common ratio to the fourth term

• Subtract the common ratio from the fourth term

• Multiply the fourth term by the common ratio

• Divide the fourth term by the common ratio

What is the fifth term of the sequence?

• Positive eight

• Negative four

• Negative eight

• Positive four