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In which of the following situations, do...

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.

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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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