Recursive Functions and Sequences

The video tutorial explains recursive functions, starting with a definition and moving on to how they work. It uses a specific example where F(1) = 5 and F(x) = F(x-1) - 3 to illustrate how each term in the sequence is calculated based on the previous term. The tutorial demonstrates the calculation of terms in the sequence and highlights that each successive term decreases by three. The explanation is supported by examples to ensure understanding.

What is the initial value of the recursive function F?

• F(1) = 3

• F(1) = 5

• F(1) = -3

• F(1) = 0

What is a key characteristic of a recursive function?

• It does not depend on any other terms.

• It requires the value of the previous term to find the current term.

• It only works for arithmetic sequences.

• It requires the value of the next term to find the current term.

How do you calculate F(3) in the given recursive function?

• By dividing F(2) by 3

• By adding 3 to F(2)

• By subtracting 3 from F(2)

• By multiplying F(2) by 3

What does the recursive rule F(x) = F(x-1) - 3 imply?

• Each term is the same as the previous term.

• Each term is 3 less than the previous term.

• Each term is 3 times the previous term.

• Each term is 3 more than the previous term.

What is the value of F(2) based on the recursive rule?

• F(2) = 8

• F(2) = -1

• F(2) = 5

• F(2) = 2

How does each successive term in the sequence change?

• It remains constant.

• It decreases by 3.

• It doubles.

• It increases by 3.

If F(1) = 5, what is F(4) using the recursive rule?

• F(4) = -1

• F(4) = 2

• F(4) = 0

• F(4) = -4

What is the pattern observed in the sequence generated by the recursive function?

• Each term is 3 times the previous term.

• Each term is the same as the previous term.

• Each term is 3 less than the previous term.

• Each term is 3 more than the previous term.