four arithmetic means between 8 and 23.
Answer (1)
Answer:To find four arithmetic means between 8 and 23, you need to first determine the common difference in an arithmetic sequence.Step-by-step explanation:1. **Calculate the common difference:** The sequence has 6 terms in total (8, 4 means, 23). The common difference \(d\) can be found using: \[ d = \frac{\text{Last term} - \text{First term}}{\text{Number of intervals}} \] Here, the number of intervals between the terms is 5. \[ d = \frac{23 - 8}{5} = \frac{15}{5} = 3 \]2. **Construct the sequence:** Start with 8 and add the common difference \(d\) iteratively: - 1st mean: \(8 + 3 = 11\) - 2nd mean: \(11 + 3 = 14\) - 3rd mean: \(14 + 3 = 17\) - 4th mean: \(17 + 3 = 20\) The sequence with the four arithmetic means is: **8, 11, 14, 17, 20, 23**.
