Fibonacci and Geometric Sequences

Teacher MJ introduces different types of sequences: arithmetic, geometric, harmonic, and Fibonacci. Each type is explained with examples, showing how to identify the sequence type and find the next term. Arithmetic sequences involve addition or subtraction, geometric sequences involve multiplication or division, harmonic sequences involve operations in the denominator, and Fibonacci sequences involve adding consecutive terms. The video concludes with a call to action for students to practice identifying sequences.

Which operation is used to identify an arithmetic sequence?

• Reciprocal

• Addition or Subtraction

• Multiplication

• Division

In an arithmetic sequence, if the first term is 8 and the common difference is 8, what is the fourth term?

• 40

• 16

• 24

• 32

What is the common ratio in a geometric sequence if the first term is 1/3 and the second term is 1/9?

• 1/9

• 1/2

• 1/6

• 1/3

If a geometric sequence starts with 1/3 and has a common ratio of 1/3, what is the fourth term?

• 1/81

• 1/27

• 1/243

• 1/729

In a Fibonacci sequence, if the first two terms are 8 and 13, what is the fourth term?

• 55

• 89

• 34

• 21

How do you determine the next term in a Fibonacci sequence?

• Divide the last two terms

• Subtract the last two terms

• Add the last two terms

• Multiply the last two terms

What operation is used in a harmonic sequence?

• Multiplication in the denominator

• Addition in the numerator

• Subtraction in the numerator

• Addition or subtraction in the denominator

In a harmonic sequence, if the first term is 1/24 and the common difference in the denominator is 4, what is the fourth term?

• 1/4

• 1/8

• 1/12

• 1/16

In the final geometric sequence example, what is the common ratio if the sequence alternates between positive and negative terms?

• 3

• -3

• 2

• -2

What is the next term in the sequence 6, -18, 54, -162?

• -972

• 972

• 486

• -486