1. The Renard Series (R-Series): These series are based on the $n$-th root of 10. The common basic series established by international standards (ISO 3) are:
• R5 series: Based on the 5th root of 10 ($\approx 1.58$). Steps are approximately 60% apart.
• R10 series: Based on the 10th root of 10 ($\approx 1.26$). Steps are approximately 25% apart.
• R20 series: Based on the 20th root of 10 ($\approx 1.12$). Steps are approximately 12% apart.
• R40 series: Based on the 40th root of 10 ($\approx 1.06$). Steps are approximately 6% apart.
2. Evaluating the Options: Looking at the standard definitions:
• R5, R10, and R20 are all fundamental, internationally recognized basic series of preferred numbers.
• R15 is not a standard basic Renard series. While one could mathematically calculate a 15th root of 10, it is not used in the standardized system of preferred numbers for engineering design.
3. Importance of Geometric Progression: Using these series allows for a constant percentage increase between successive sizes (e.g., motor power ratings, bolt diameters, or container volumes). This prevents "gaps" in the market and ensures that the ratio of the "next size up" is consistent regardless of the scale.