Question

Which of the sequences is an arithmetic sequence?
1, - 2,3, -4,5,...
-3, -10, -17, -24, -31,..
3, 6, 9, 15,24,...
1,8, 16,24, 32,...

Answer 1

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Let's analyze the given sequences:

1. **Sequence: 1, -2, 3, -4, 5,...**
- Differences: -2 - 1 = -3, 3 - (-2) = 5, -4 - 3 = -7, 5 - (-4) = 9
- The differences are not constant, so this is not an arithmetic sequence.

2. **Sequence: -3, -10, -17, -24, -31...**
- Differences: -10 - (-3) = -7, -17 - (-10) = -7, -24 - (-17) = -7, -31 - (-24) = -7
- The difference is consistently -7, so this is an arithmetic sequence.

3. **Sequence: 3, 6, 9, 15, 24,...**
- Differences: 6 - 3 = 3, 9 - 6 = 3, 15 - 9 = 6, 24 - 15 = 9
- The differences are not constant, so this is not an arithmetic sequence.

4. **Sequence: 1, 8, 16, 24, 32,...**
- Differences: 8 - 1 = 7, 16 - 8 = 8, 24 - 16 = 8, 32 - 24 = 8
- The differences are not constant (the first difference is 7 while the others are all 8), so this is not an arithmetic sequence.

The only arithmetic sequence among the given options is **-3, -10, -17, -24, -31...**, where the common difference is -7.