Understanding Geometric Sequences

The video tutorial explains geometric sequences, starting with an initial number and multiplying each term by a fixed non-zero number, known as the common ratio. The instructor demonstrates how to calculate successive terms and the common ratio using examples. The video also covers how to identify geometric sequences and verify the common ratio through division of successive terms.

What is the first step in constructing a geometric sequence?

• Add a fixed number to each term

• Multiply the first term by a fixed number

• Subtract a fixed number from each term

• Divide the first term by a fixed number

In a geometric sequence, what is the term used to describe the fixed number by which each term is multiplied?

• Common divisor

• Common factor

• Common ratio

• Common difference

How do you find the common ratio in a geometric sequence?

• By dividing two successive terms

• By multiplying two successive terms

• By subtracting two successive terms

• By adding two successive terms

If the first term of a geometric sequence is 5 and the common ratio is 1/7, what is the second term?

• 5/343

• 5/14

• 5/49

• 5/7

What is the third term in a geometric sequence where the first term is 5 and the common ratio is 1/7?

• 5/14

• 5/343

• 5/7

• 5/49

In the sequence 3, 6, 12, 24, 48, what is the common ratio?

• 6

• 4

• 2

• 3

What operation is performed to go from one term to the next in a geometric sequence?

• Subtraction

• Addition

• Multiplication

• Division

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

• 12

• 24

• 48

• 96

What would happen if the common ratio in a geometric sequence was not constant?

• It would still be a geometric sequence

• It would become an arithmetic sequence

• It would not be a geometric sequence

• It would become a harmonic sequence

In a geometric sequence, if the common ratio is 2, what is the result of dividing the third term by the second term?

• 4

• 3

• 2

• 1