Question

Practice Arithmetic Sequences 4-6 Describe the pattern in each sequence. Then find the next two terms of the sequence. 1. 3, 6, 12, 24,... 4. 9.9, 8.8, 7.7, 6.6, ... 7. 7, 11, 15, 19, ... 2. 9, 15, 21, 27, ... 13. 12, 23, 34, 45, ... 5. 1.5, 4.5, 13.5, 40.5, ... 8. 67, 60, 53, 46, ... 3. 1.5, 2.25, 3, 3.75, ... 14. 2,4,7,9,... 6. 40, 20, 10, 5, ... Tell whether the sequence is arithmetic. If it is, identify the common difference. 10. 4, 8, 12, 16, ... 11. -11,5, 0, 6, ... 12. 4, 8, 16, 32, ... 9. 12, 7, 2,-3, ... 15. 1,3,9,27,...​

Answer 1

Let's analyze and find the next two terms for each sequence:

1. \(3, 6, 12, 24, ...\): The pattern is doubling each time. Next terms: 48, 96.

2. \(9, 15, 21, 27, ...\): The common difference is 6. Next terms: 33, 39.

3. \(1.5, 2.25, 3, 3.75, ...\): The pattern is multiplying by 1.5. Next terms: 4.5, 6.75.

4. \(9.9, 8.8, 7.7, 6.6, ...\): The common difference is -1.1. Next terms: 5.5, 4.4.

5. \(1.5, 4.5, 13.5, 40.5, ...\): The pattern is multiplying by 3. Next terms: 121.5, 364.5.

6. \(40, 20, 10, 5, ...\): The pattern is dividing by 2. Next terms: 2.5, 1.25.

7. \(7, 11, 15, 19, ...\): The common difference is 4. Next terms: 23, 27.

8. \(67, 60, 53, 46, ...\): The common difference is -7. Next terms: 39, 32.

9. \(12, 7, 2, -3, ...\): The common difference is -5. Next terms: -8, -13.

10. \(4, 8, 12, 16, ...\): The common difference is 4. It is an arithmetic sequence.

11. \(-11, 5, 0, 6, ...\): It is not an arithmetic sequence.

12. \(4, 8, 16, 32, ...\): The common ratio is 2. It is a geometric sequence.

13. \(12, 23, 34, 45, ...\): The common difference is 11. It is an arithmetic sequence.

14. \(2, 4, 7, 9, ...\): It is not an arithmetic sequence.

15. \(1, 3, 9, 27, ...\): The common ratio is 3. It is a geometric sequence.