Final answer:
The next three terms for the arithmetic sequence A are approximately 16.44, 10.22, and 4. For the increasing arithmetic sequence B with changing differences, they are approximately 58.05, 62.19, and 66.60. The geometric sequence C's terms are 640, 1280, and 2560.
Step-by-step explanation:
To write the next three terms for each sequence, we first need to determine the pattern that each sequence follows.
- Sequence A: 34.68, 28.44, 22.66 - This appears to be an arithmetic sequence where each term decreases by 6.22 (28.44 - 34.68 = -6.24 and 22.66 - 28.44 = -5.78, suggesting a slight error in the second difference). Assuming the pattern of decreasing by approximately 6.22, the next three terms would be 16.44, 10.22, and 4.
- Sequence B: 47.25, 50.58, 54.18 - This sequence appears to be increasing each time. The differences are 3.33 and 3.60, suggesting an increasing sequence where each difference could be an increment from the prior difference. If the increment is approximately 0.27, the next differences could be 3.87, 4.14, and 4.41. Therefore, the next three terms would be approximately 58.05, 62.19, and 66.60.
- Sequence C: 80, 160, 320 - This is clearly a geometric sequence where each term is multiplied by 2. Therefore, the next three terms are 640, 1280, and 2560.
In summary, for each sequence, the patterns were identified as an arithmetic sequence, an increasing arithmetic sequence with changing differences, and a geometric sequence respectively.