Question

Which of the sequences is an arithmetic sequence?
v
1, 5, 10, 15, 20, ...
-20, -27, -34, -41, -48,..
• 12, -24,36, -48, 60, ...
154, 71, 8, 5, 2,...

Answer 1

An arithmetic sequence is one in which the difference between consecutive terms is constant.

Let's examine the sequences one by one:

1. **1, 5, 10, 15, 20, ...**
- The differences are:
- 5 - 1 = 4
- 10 - 5 = 5
- 15 - 10 = 5
- 20 - 15 = 5
- The differences are not constant (the first difference is 4 while the others are 5). This is **not** an arithmetic sequence.

2. **-20, -27, -34, -41, -48, ..**
- The differences are:
- -27 - (-20) = -7
- -34 - (-27) = -7
- -41 - (-34) = -7
- -48 - (-41) = -7
- The differences are constant, equal to -7. This is an **arithmetic sequence**.

3. **12, -24, 36, -48, 60, ...**
- The differences are:
- -24 - 12 = -36
- 36 - (-24) = 60
- -48 - 36 = -84
- 60 - (-48) = 108
- The differences are not constant. This is **not** an arithmetic sequence.

4. **154, 71, 8, 5, 2,...**
- The differences are:
- 71 - 154 = -83
- 8 - 71 = -63
- 5 - 8 = -3
- 2 - 5 = -3
- The differences are not constant. This is **not** an arithmetic sequence.

In conclusion, the only arithmetic sequence from the provided options is:
- **-20, -27, -34, -41, -48,...**