In which of the following situations, does the list of numbers involved make an arithmetic progression, and why ?
the taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.

Answer

To determine whether the taxi fare situation forms an arithmetic progression (AP), we will analyze the fare structure step by step.

### Step 1: Understand the Fare Structure
The fare for the taxi is structured as follows:
- For the first kilometer, the fare is Rs. 15.
- For each additional kilometer, the fare is Rs. 8.

### Step 2: Calculate the Fare for Each Kilometer
Let's calculate the total fare for the first few kilometers:

- **1 km:**
- Fare = Rs. 15
- **2 km:**
- Fare = Rs. 15 (first km) + Rs. 8 (second km) = Rs. 23
- **3 km:**
- Fare = Rs. 15 (first km) + Rs. 8 (second km) + Rs. 8 (third km) = Rs. 31
- **4 km:**
- Fare = Rs. 15 (first km) + Rs. 8 (second km) + Rs. 8 (third km) + Rs. 8 (fourth km) = Rs. 39

### Step 3: List the Fares
Now we can list the fares for the first four kilometers:
- 1 km: Rs. 15
- 2 km: Rs. 23
- 3 km: Rs. 31
- 4 km: Rs. 39

### Step 4: Check the Differences
Next, we will check the differences between consecutive fares:
- Difference between 2 km and 1 km: 23 - 15 = Rs. 8
- Difference between 3 km and 2 km: 31 - 23 = Rs. 8
- Difference between 4 km and 3 km: 39 - 31 = Rs. 8

### Step 5: Conclusion
Since the difference between each consecutive fare is the same (Rs. 8), we can conclude that the list of fares forms an arithmetic progression.

### Final Answer
Yes, the taxi fare after each kilometer forms an arithmetic progression because the difference between consecutive fares is constant (Rs. 8).

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