Toothpick Sequence and Formulas

The video tutorial explains how to determine the number of toothpicks needed to form the 50th figure in a sequence. It begins by analyzing the first few figures to identify a pattern, then generalizes this pattern to find a formula for any nth term. An alternative approach using a hypothetical 0th term is also discussed. Finally, the tutorial applies these methods to calculate the number of toothpicks in the 50th figure, confirming the result with both approaches.

What is the main question being addressed in the video?

• How to calculate the area of a figure

• How to build a house with toothpicks

• How many toothpicks are needed for the 50th figure

• How to draw figures with toothpicks

What is the number of toothpicks in the first figure?

• 5

• 7

• 6

• 8

How many toothpicks are added to each subsequent figure in the sequence?

• Six

• Five

• Four

• Three

How many toothpicks are in the second figure?

• 10

• 11

• 12

• 13

What is the formula used to calculate the number of toothpicks in the nth figure?

• n plus 5

• n times 6

• n times 5 plus 1

• n minus 1 times 5 plus 6

What is the number of toothpicks in the third figure?

• 18

• 17

• 16

• 15

What is the alternative method introduced to understand the sequence?

• Using a 1st term

• Using a 3rd term

• Using a 0th term

• Using a 2nd term

What is the number of toothpicks in the fourth figure?

• 23

• 22

• 21

• 20

How many toothpicks are in the 50th figure according to the formula?

• 252

• 253

• 251

• 250

What is the simplified formula for the nth term using the 0th term method?

• n times 5

• 5 plus n

• n plus 1

• 1 plus 5 times n