Understanding Sequences: Arithmetic and Geometric

The video tutorial explores arithmetic and geometric sequences, explaining how to identify them and differentiate between the two. It covers the concepts of common differences and common ratios, and demonstrates how to write equations for sequences using exponents. The tutorial includes examples and practice problems to reinforce understanding.

What is the common difference in an arithmetic sequence?

• The number added to each term to get the next term

• The number subtracted from each term to get the next term

• The number each term is multiplied by to get the next term

• The number each term is divided by to get the next term

In a geometric sequence, what operation is used to move from one term to the next?

• Addition

• Multiplication

• Division

• Subtraction

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

• By multiplying the first two terms

• By dividing the second term by the first

• By subtracting the first term from the second

• By adding the first two terms

What is the role of the exponent in the equation for a geometric sequence?

• It indicates how many times the common ratio is multiplied

• It represents the number of terms in the sequence

• It determines the common difference

• It shows the starting value of the sequence

If the first term of a geometric sequence is 3 and the common ratio is 4, what is the fifth term?

• 48

• 192

• 768

• 372

What is the starting value in a geometric sequence?

• The common ratio

• The term before the first term

• The first term of the sequence

• The exponent value

How do you determine the starting value if it is not the first term?

• By subtracting the common ratio from the first term

• By adding the common ratio to the first term

• By multiplying the first term by the common ratio

• By dividing the first term by the common ratio

In a sequence where each term is multiplied by 0.5, what happens to the terms?

• They alternate between increasing and decreasing

• They increase

• They decrease

• They remain constant

What is the common ratio if the sequence starts with 2/3 and the next term is 2/9?

• 3/2

• 2/3

• 1/3

• 1/2

How can you verify the rule of a sequence with fractions?

• By adding the fractions

• By multiplying the fractions

• By dividing the fractions

• By subtracting the fractions