Answer:
**Arithmetic Means:**
1. **Find the arithmetic mean between 8 and 20:**
- The arithmetic mean (A.M.) in an arithmetic sequence is the average of two consecutive terms.
- \[ A.M. = \frac{8 + 20}{2} \]
2. **Calculate four arithmetic means between 2 and 32:**
- In an arithmetic sequence, the common difference is the difference between consecutive terms.
- Calculate the common difference (\(d\)) and then find the four arithmetic means.
**Geometric Means (Mean Proportion):**
1. **Find the geometric mean between 2 and 8:**
- The geometric mean (G.M.) in a geometric sequence is the square root of the product of two consecutive terms.
- \[ G.M. = \sqrt{2 \times 8} \]
2. **Determine a, b, and c if \(x; a; b; c; \frac{x}{16}\) forms a geometric sequence:**
- In a geometric sequence, the common ratio is the ratio between consecutive terms.
- Set up equations based on the given sequence and solve for \(a\), \(b\), and \(c\).
Answer:
One method is to calculate the arithmetic mean. To do this, add up all the values and divide the sum by the number of values. For example, if there are a set of “n” numbers, add the numbers together for example: a + b + c + d and so on.
