Graicuna's formula suggests that

The correct answer is: D. the number of subordinates increases in arithmetic progression while the number of relations increase in geometric progression.

Graicuna's formula is a mathematical model that predicts the number of subordinates and relations that a person will have at a given point in their career. The formula states that the number of subordinates will increase in arithmetic progression, while the number of relations will increase in geometric progression. This means that the number of subordinates will increase by a constant amount each time, while the number of relations will increase by a constant factor each time.

This formula is based on the observation that people tend to have more subordinates than relations. This is because subordinates are typically people who are directly under the authority of the person, while relations are typically people who are not directly under the authority of the person, but who are still connected to the person through some other means, such as friendship or family.

The formula has been shown to be accurate in predicting the number of subordinates and relations that people have at different points in their careers. It is a useful tool for people who are trying to plan their careers and for organizations that are trying to understand the structure of their workforce.

Here is a brief explanation of each option:

• Option A: The number of subordinates and relations both increase in arithmetic progression. This is not the case, as the number of relations increases in geometric progression, while the number of subordinates increases in arithmetic progression.
• Option B: The number of subordinates increases in geometric progression and number of relations increases in arithmetic progression. This is not the case, as the number of relations increases in geometric progression, while the number of subordinates increases in arithmetic progression.
• Option C: The number of subordinates and relations both increase in geometric progression. This is not the case, as the number of relations increases in geometric progression, while the number of subordinates increases in arithmetic progression.
• Option D: The number of subordinates increases in arithmetic progression while the number of relations increase in geometric progression. This is the correct answer, as it is the only option that is consistent with Graicuna's formula.