Question

Which of these are arithmetic sequences?

3, 6, 9, 12, ...
-2, 1, 4, 7, ...
27, 27.75, 28.5, 29.25, ...
1, 2, 3, 5, ...
1, 3, 9, 27, ...
1, 1.30, 1.60, 1.90, ...
2, 12, 22, 32, ...
2, -2, -6, -10, ...
6, 16, 116, 1116, ...
2, 11, 36, 45, ...

Answer 1

The arithmetic sequences among the given sequences are: 3, 6, 9, 12, ...; -2, 1, 4, 7, ...; 27, 27.75, 28.5, 29.25, ...

Step-by-step explanation:

Arithmetic sequences are sequences in which the difference between consecutive terms is constant. Let's analyze each given sequence to determine if it is arithmetic:

1. Sequence: 3, 6, 9, 12, ... -> This is an arithmetic sequence with a common difference of 3.
2. Sequence: -2, 1, 4, 7, ... -> This is an arithmetic sequence with a common difference of 3.
3. Sequence: 27, 27.75, 28.5, 29.25, ... -> This is an arithmetic sequence with a common difference of 0.75.
4. Sequence: 1, 2, 3, 5, ... -> This is not an arithmetic sequence, the difference between consecutive terms is not constant.
5. Sequence: 1, 3, 9, 27, ... -> This is not an arithmetic sequence, the ratio between consecutive terms is not constant.
6. Sequence: 1, 1.30, 1.60, 1.90, ... -> This is an arithmetic sequence with a common difference of 0.30.
7. Sequence: 2, 12, 22, 32, ... -> This is an arithmetic sequence with a common difference of 10.
8. Sequence: 2, -2, -6, -10, ... -> This is an arithmetic sequence with a common difference of -4.
9. Sequence: 6, 16, 116, 1116, ... -> This is not an arithmetic sequence, the difference between consecutive terms is not constant.
10. Sequence: 2, 11, 36, 45, ... -> This is not an arithmetic sequence, the difference between consecutive terms is not constant.