Question

A multi-level marketing scheme starts with 4 members, and each of these members have to recruit 5 more members in their "downline" to move up a level and earn a greater commission, and then those they recruit must recruit 5 more members, and so on, so to be successful, the scheme has to grow by a factor of 5 each level.

- The scheme has 6 levels. How many total people need to be involved in the entire scheme for the original members to make it to the top level?
- How many people are needed at the bottom level of the scheme?

Answer 1

The total number of people required in a 6-level multi-level marketing scheme, where each person must recruit 5 others to progress, is 15,624. The number of people needed at the bottom level, which is the 6th level, is 3,125.

Step-by-step explanation:

To find the total number of people involved in the entire scheme, we recognize that this is a problem of geometric progression, where each level grows by a factor of 5. We have 4 original members, and each of these members recruit 5 more members, and this pattern continues for each subsequent level. In mathematical terms, the total number of members at each level can be found using the formula for the sum of a geometric series:

Total number of people = 4 × (1 – 56) / (1 – 5)

This simplifies to:
Total number of people = 4 × (1 – 15,625) / (–4)
Total number of people = 4 × 15,624 / 4
Total number of people = 15,624

To find the number of people needed at the bottom level of the scheme, we simply calculate the number of people in the 6th level, as it is the last level. Thus, we need to take the number of members the last person in the 5th level recruited:

People at the bottom level = 55
People at the bottom level = 3,125