Patterns in sequences 2 | Linear equations | Algebra I | Khan Academy

TL;DR

The video explains a sequence of toothpick figures and how to determine the number of toothpicks in the 50th figure using a formula.

Transcript

Our question asks us, how many toothpicks will be needed to form the 50th figure in this sequence? So let's look at this sequence. So the first figure in our sequence-- they look like little houses-- how many toothpicks are here? We have one, two, three, four, five, six toothpicks. So our first object here, or our first figure, has six toothpicks. ... Read More

Key Insights

• 👶 The toothpick figures sequence follows a pattern of adding five toothpicks to each new figure.
• 💭 The formula for finding the number of toothpicks in the nth figure is 1 + 5n.
• #️⃣ The number of toothpicks in the 50th figure is determined to be 251 using the formula.

Questions & Answers

Q: What is the pattern observed in the toothpick figures sequence?

Each new figure adds five additional toothpicks to the previous one, forming a linear progression.

Q: How can the formula for finding the number of toothpicks in the nth figure be derived?

By analyzing the pattern, it is found that the formula is 1 + 5n, where n represents the figure number.

Q: Why is the initial figure written as 1 + 5 instead of just 6?

Writing it as 1 + 5 emphasizes that the first figure has one 5, while the second figure has two 5's, and so on, following the pattern.

Q: How can the number of toothpicks in the 50th figure be calculated using the formula?

Plugging in n = 50 into the formula (1 + 5n), the calculation becomes 1 + 5(50), resulting in 251 toothpicks.

Summary & Key Takeaways

• The video discusses a sequence of toothpick figures, where each new figure adds five additional toothpicks to the previous one.

• By observing the pattern, it is determined that the formula for finding the number of toothpicks in the nth figure is 1 + 5n.

• To find the number of toothpicks in the 50th figure, the formula is applied, resulting in 251 toothpicks.