Understanding Sequences: Arithmetic, Geometric, or Neither

The video tutorial explains how to determine if a sequence is arithmetic, geometric, or neither. It reviews the concepts of common difference and common ratio, providing examples for each type of sequence. The tutorial demonstrates how to analyze sequences by generating terms and using formulas to identify patterns. It concludes with an example of a sequence that is neither arithmetic nor geometric.

What is the main characteristic of an arithmetic sequence?

• It has a variable difference.

• It has no pattern.

• It has a common difference.

• It has a common ratio.

How do you determine if a sequence is geometric?

• By checking if the terms are subtracted by a constant.

• By checking if the terms are multiplied by a constant.

• By checking if the terms are divided by a constant.

• By checking if the terms are added by a constant.

In the sequence 'A sub N = 5 - 2N', what is the common difference?

• -2

• -5

• 2

• 5

What is the common ratio in the sequence where N is 1, 2, 3, and so on, and the terms are 6, 18, 54?

• 3

• 2

• 9

• 6

If a sequence has a common ratio of 3, what type of sequence is it?

• Arithmetic

• Geometric

• Neither

• Both

What happens to the terms in a sequence that is neither arithmetic nor geometric?

• They have a common difference.

• They have a common ratio.

• They have no consistent pattern.

• They are constant.

In the sequence where N = 1, 2, 3, and the terms are 3/3, 3/4, 3/5, what is the pattern?

• Both numerator and denominator increase by 1.

• The numerator increases by 1.

• The denominator increases by 1.

• There is no pattern.

Why is the sequence 3/3, 3/4, 3/5 not arithmetic?

• It has a common ratio.

• Both numerator and denominator change.

• It has a common difference.

• The denominator changes but the numerator does not.

Why is the sequence 3/3, 3/4, 3/5 not geometric?

• The terms are constant.

• The ratio between terms is not constant.

• It has a common difference.

• It has a common ratio.

What is the key difference between arithmetic and geometric sequences?

• Both have a common ratio.

• Arithmetic sequences have a common difference, geometric have a common ratio.

• Both have a common difference.

• Arithmetic sequences have a common ratio, geometric have a common difference.