Geometric series word problems: swing | Algebra 2 | Khan Academy

TL;DR

A monkey swings from a tree with each swing passing through an arc half the length of the previous swing, and the total distance swung can be calculated using a geometric series.

Transcript

• [Instructor] We're told a monkey is swinging from a tree. On the first swing, she passes through an arc of 24 meters. With each swing, she passes through an arc 1/2 the length of the previous swing. So what's going on here? Let's say this is the top of the rope or the vine that the monkey is swinging from. And so on that first swing, I like to dr... Read More

Key Insights

• 🙈 The monkey's swings follow a consistent pattern, with each swing being half the length of the previous swing.
• 😑 The total distance swung by the monkey can be expressed as a geometric series.
• 🙈 The formula for a finite geometric series can be used to evaluate the total distance swung by the monkey.
• 🤒 The total distance swung by the monkey on the 25th swing is approximately 48 meters.
• 🤒 The first term in the geometric series is 24 meters and the common ratio is 1/2.

Questions & Answers

Q: How does the length of the monkey's swings change with each swing?

With each swing, the length of the monkey's swing is halved compared to the previous swing.

Q: How can the total distance swung by the monkey be expressed as a geometric series?

The total length of the monkey's swings can be expressed as a geometric series, where the first term is 24 meters and the common ratio is 1/2.

Q: What is the formula for calculating the sum of the first n terms of a geometric series?

The sum of the first n terms of a geometric series can be calculated using the formula a(1-r^n) / (1-r), where a is the first term and r is the common ratio.

Q: How can the total distance swung by the monkey be evaluated?

Using the formula for a finite geometric series, the total distance swung can be evaluated by plugging in the values for the first term, common ratio, and the desired number of swings.

Summary & Key Takeaways

• A monkey swings from a tree, passing through arcs of decreasing length with each swing.

• The total length of the monkey's swings can be expressed as a geometric series.

• The formula for a finite geometric series can be used to evaluate and calculate the total distance swung by the monkey.