Exploring Arithmetic and Geometric Sequences

The video tutorial explains the concepts of arithmetic and geometric sequences. It begins by defining an arithmetic sequence as a list of numbers where a constant value, called the common difference, is added to each term to get the next. The tutorial then introduces geometric sequences, where each term is multiplied by a constant value, known as the common ratio, to obtain the next term. Examples are provided to illustrate both types of sequences, and methods for identifying them are discussed. The video concludes with practice problems to reinforce the learning objectives.

What is added to each term to get the next term in an arithmetic sequence?

• Next term

• Previous term

• Common ratio

• Common difference

What is the common difference in an arithmetic sequence where each term increases by 4?

• 8

• 6

• 2

• 4

What operation is performed on each term to get the next term in a geometric sequence?

• Addition

• Division

• Subtraction

• Multiplication

How is the common ratio of a geometric sequence determined?

• By multiplying consecutive terms

• By dividing a term by its preceding term

• By subtracting consecutive terms

• By adding consecutive terms

What is the common ratio in a sequence where each term is triple the previous term?

• 2

• 3

• -3

• 1/3

How do you identify an arithmetic sequence using the first three terms?

• By adding them

• By finding the common difference

• By multiplying them

• By dividing them

What indicates a geometric sequence when examining the first three terms?

• Constant division factor

• Constant multiplication factor

• Constant subtraction

• Constant addition

What is the common ratio in a geometric sequence where each term is half of the previous term?

• 2

• -1/2

• 1/2

• -2

In a geometric sequence, if the common ratio is negative, how do the sequence terms behave?

• They increase

• They decrease

• They alternate between positive and negative

• They remain constant

If a sequence has a common ratio of -2, what is the nature of this sequence?

• Geometric with positive growth

• Static

• Arithmetic

• Geometric with negative growth