Understanding Sequences and Factorials

The video tutorial explains how to determine the first four terms of three different sequences using given formulas. It covers the calculation of factorials and powers, simplifying fractions, and using scientific calculators for precise results. The tutorial also highlights the differences between similar-looking formulas and provides step-by-step instructions for each sequence.

What is the first step in determining the first term of a sequence given the formula a_n = (n+2)! / 3^n?

• Simplify the expression

• Substitute 1 for n

• Divide by 3 to the power of n

• Calculate 3 factorial

How do you simplify the expression for the second term in the sequence?

• Divide by 2

• Cancel common factors

• Multiply by 3

• Add 1 to the result

What is the result of simplifying the third term in the sequence?

• 5/2

• 8/3

• 3/1

• 40/9

Which tool can be used to simplify the expression for the fourth term?

• Ruler

• Protractor

• Graphing Paper

• Desmos Scientific Calculator

What is the difference between the two sequence formulas discussed in the last section?

• One uses powers, the other uses roots

• One uses addition, the other uses subtraction

• One uses multiplication, the other uses division

• One uses factorial of 2n, the other uses 2 times n factorial

How do you calculate the first term for the sequence with the formula factorial of 2n?

• Calculate 2 factorial

• Substitute 2 for n

• Multiply by 3

• Add 2 to the result

What is the result of the second term for the sequence with the formula factorial of 2n?

• 6

• 24

• 8

• 12

How do you determine the third term for the sequence with the formula 2 times n factorial?

• Multiply by 4

• Calculate 3 factorial

• Add 1 to the result

• Divide by 2

What is the result of the fourth term for the sequence with the formula 2 times n factorial?

• 6

• 12

• 24

• 48

Which sequence formula results in larger terms as n increases?

• Both result in the same terms

• Factorial of 2n

• 2 times n factorial

• Neither results in larger terms