Understanding Sequences and Factorials

The video tutorial explains how to determine the indicated terms of a sequence using a given formula. It provides detailed calculations for the first four terms (a₁, a₂, a₃, a₄) of the sequence, demonstrating the use of factorials and simplification techniques. Each term is calculated by substituting the value of n into the formula, simplifying the factorials, and reducing the fractions. The tutorial emphasizes finding common factors to simplify the results.

What is the formula used to determine the terms of the sequence?

• n factorial divided by n squared

• n plus two factorial divided by two n squared minus n plus six

• n squared plus two divided by n factorial

• n plus two divided by n squared minus n

How is the factorial of a number calculated?

• By dividing the number by two

• By adding all numbers up to that number

• By multiplying all numbers up to that number

• By subtracting one from the number

What is the value of a₁ in the sequence?

• 2/3

• 3/7

• 6/7

• 1/2

What is the value of a₂ in the sequence?

• 4

• 1

• 2

• 3

Which common factor is used to simplify a₂?

• 6

• 8

• 4

• 12

What is the value of a₃ in the sequence?

• 40/21

• 20/7

• 40/7

• 21/40

What common factor is used to simplify a₃?

• 2

• 5

• 4

• 3

What is the value of a₄ in the sequence?

• 340/17

• 300/17

• 320/17

• 360/17

What is the only common factor between the numerator and denominator in a₄?

• 4

• 5

• 3

• 2

What is the factorial of 6?

• 720

• 360

• 120

• 240