Lesson 4
1. Lesson 4
1.5. Explore
Module 1: Sequences and Series
Explore
A pyramid scheme is a fraudulent money-making scam. These schemes are illegal because they deceive people by promising huge sums of money. The idea of a pyramid scheme is based on a person or group of people recruiting other people. Those who have been recruited pay a fee to the recruiter.
The recruited individuals, in turn, recruit more people who also pay a fee. The fees are distributed to those who are higher up in the pyramid. To make money in this scheme, you must have many levels of recruited individuals beneath you.
The illustration shows an example of how a pyramid scheme works. In this example each recruited person recruits six other people. Do you think this practice can continue on forever?
The number of people recruited at each level forms a sequence. In this lesson you will investigate sequences of this kind. You will discover whether a pyramid scheme is sustainable. You will determine the general term for these sequences, and you will use the general term to solve problems related to finance and other applications.
You already saved Module 1 Glossary Terms in your course folder. In this lesson, you will define the following terms, and maybe others, in your copy of Module 1 Glossary Terms:
- geometric sequence
- common ratio
- compound interest
Geometric Sequence and Common Ratio
As you folded paper in Math Lab, you might have noticed the pattern, or sequence, related to the number of layers after each fold: 1, 2, 4, 8, ….
Can you see a common difference between each term in the sequence? You have already studied arithmetic sequences in which terms always increase or decrease by the same value. In this example, the difference between each term changes; therefore, there is no common difference and the sequence is not arithmetic.
In this sequence, you multiply each value by 2 to obtain the value of the next term. This is an example of a geometric sequence. In this case, the constant, 2, is known as the common ratio.
