Understanding Sequences and Closed Formulas

The video tutorial explains how to write the first five terms of a sequence starting with a sub zero, using a recursive definition. It then guides viewers through determining a closed formula for the sequence. The process involves calculating initial terms, identifying a pattern, and verifying the closed formula using factorial numbers. The tutorial concludes with a confirmation of the formula's correctness.

What is the initial value of a sub zero in the given sequence?

• 2

• 1

• 4

• 3

How is a sub one calculated in the sequence?

• 1 times a sub zero

• 2 times a sub zero

• 3 times a sub zero

• 4 times a sub zero

What is the value of a sub two in the sequence?

• 12

• 9

• 6

• 3

How do you calculate a sub three using the recursive formula?

• 3 times a sub two

• 3 times a sub one

• 3 times a sub zero

• 3 times a sub three

What is the value of a sub four in the sequence?

• 36

• 54

• 18

• 72

What pattern is used to find the closed formula for the sequence?

• Fibonacci sequence

• Arithmetic progression

• Geometric progression

• Factorial numbers

What is the closed formula derived for the sequence?

• a sub n equals 3 times n factorial

• a sub n equals 4 times n factorial

• a sub n equals 2 times n factorial

• a sub n equals n factorial

How is the closed formula verified for a sub zero?

• By checking a sub zero equals 3 times 1

• By checking a sub zero equals 3 times 0 factorial

• By checking a sub zero equals 3 times 2

• By checking a sub zero equals 3 times 3

What is the value of a sub one using the closed formula?

• 12

• 9

• 6

• 3

What is the value of a sub three using the closed formula?

• 12

• 18

• 24

• 30