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As the name suggests, a pyramid scheme is rarely a sound investment. In spite of this, every few years there’s an article in the news about people who have been duped by such a scheme. So what exactly is a pyramid scheme, and do people actually make money from them?

In this lesson, students learn about how pyramid schemes work, and use geometric sequences to model the (exponential!) growth of a pyramid scheme over time. While these investments may look appealing, a more detailed analysis will reveal why most people who put money into a pyramid scheme never recoup their investment. Pyramids may be fun for archaeologists or geometers, but when it comes to your finances, they’re a shape that’s best avoided.

### Students will

• Understand how pyramid schemes work using concrete examples
• Determine how much money a person can make from a pyramid scheme in various scenarios
• Determine the number of people required to sustain a pyramid scheme
• Explore what happens when a pyramid scheme collapses, including who makes money and who doesn’t
• Discuss whether or not it ever makes sense to invest in a pyramid scheme

### Before you begin

Students will be calculating finite sums of geometric sequences several times in this lesson. Some prior experience with these sums will be useful. In particular, they’ll have an easier time if they know the formula for the finite sum of a geometric sequence, but this knowledge isn’t required. You can either omit the formula entirely, or use this lesson as an opportunity to introduce the formula.