Understanding Recursive Functions and Arithmetic Sequences

The video tutorial explains a recursive function F(n) defined as F(n) = F(n-1) + 6, with F(1) = 8. It guides viewers through calculating the function values for n=1 to 4, identifying a pattern of adding six to each previous term. The tutorial then graphs these values, showing a linear pattern, and discusses the characteristics of arithmetic sequences, emphasizing their linear nature when plotted.

What is the initial value of the function F(n) in the recursive definition provided?

• 8

• 6

• 12

• 10

How is F(2) calculated in the recursive function F(n) = F(n-1) + 6?

• F(1) + 12

• F(1) + 10

• F(1) + 8

• F(1) + 6

What is the value of F(3) in the sequence?

• 32

• 26

• 20

• 14

What pattern is observed in the sequence of function values?

• Each term is increased by 6

• Each term is squared

• Each term is halved

• Each term is doubled

What is the value of F(4) in the sequence?

• 20

• 22

• 24

• 26

What does the graphical representation of the sequence suggest about its nature?

• It forms a line

• It forms a circle

• It forms a parabola

• It forms a curve

What is the slope of the line formed by the sequence points on the graph?

• 4

• 5

• 6

• 7

What type of sequence is represented by the function F(n) = F(n-1) + 6?

• Geometric sequence

• Arithmetic sequence

• Fibonacci sequence

• Harmonic sequence

What is the constant difference between consecutive terms in the sequence?

• 4

• 5

• 7

• 6

What clue indicates that a sequence is arithmetic when graphed?

• The points form a zigzag

• The points form a spiral

• The points form a line

• The points form a curve