Understanding Sequences: Arithmetic, Geometric, or Neither

The video tutorial explains how to determine if a sequence is arithmetic, geometric, or neither. It covers the concepts of common difference and common ratio, providing methods to identify these in sequences. The tutorial includes examples of arithmetic sequences, where a constant is added to each term, and geometric sequences, where each term is multiplied by a constant. It also discusses how to identify sequences that are neither arithmetic nor geometric.

What is the defining characteristic of an arithmetic sequence?

• A common difference between terms

• A common ratio between terms

• Terms that are squares of integers

• Terms that are cubes of integers

How can you find the common difference in an arithmetic sequence?

• By adding any term to the previous term

• By subtracting any term from the previous term

• By dividing any term by the previous term

• By multiplying any term by the previous term

In the given arithmetic sequence example, what is the common difference?

• 6

• 5

• 7

• 8

What indicates that a sequence is neither arithmetic nor geometric?

• It has neither a common difference nor a common ratio

• It has a common ratio but no common difference

• It has both a common difference and a common ratio

• It has a common difference but no common ratio

In the sequence that is neither arithmetic nor geometric, what was the result of checking for a common difference?

• The common difference was negative

• The common difference was consistent

• The common difference varied

• The common difference was zero

What is the defining characteristic of a geometric sequence?

• Terms that are squares of integers

• A common difference between terms

• A common ratio between terms

• Terms that are cubes of integers

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

• By subtracting any term from the previous term

• By multiplying any term by the previous term

• By dividing any term by the previous term

• By adding any term to the previous term

In the given geometric sequence example, what is the common ratio?

• 2

• 4

• 3

• 5

What is the result of multiplying each term by the common ratio in a geometric sequence?

• The sequence becomes a constant

• The sequence becomes neither arithmetic nor geometric

• The sequence remains geometric

• The sequence becomes arithmetic

In the geometric sequence example, what is the result of dividing the second term by the first term?

• 1

• 2

• 3

• 4