In which of the following situations , does the list of numbers of involved make an arithmetic progression , and why ?
The cost of digging a well after every metre of dogging ,when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre .

Answer

To determine whether the cost of digging a well forms an arithmetic progression (AP), we can follow these steps:

### Step 1: Identify the first term and the common difference.
- The cost of digging the first meter is Rs 150.
- The cost increases by Rs 50 for each subsequent meter.

### Step 2: List the costs for the first few meters.
- Cost for the 1st meter: Rs 150
- Cost for the 2nd meter: Rs 150 + Rs 50 = Rs 200
- Cost for the 3rd meter: Rs 200 + Rs 50 = Rs 250
- Cost for the 4th meter: Rs 250 + Rs 50 = Rs 300

### Step 3: Write the series of costs.
- The series of costs is: 150, 200, 250, 300, ...

### Step 4: Check the differences between consecutive terms.
- Difference between 2nd and 1st term: 200 - 150 = Rs 50
- Difference between 3rd and 2nd term: 250 - 200 = Rs 50
- Difference between 4th and 3rd term: 300 - 250 = Rs 50

### Step 5: Verify that the differences are constant.
- Since the difference between each pair of consecutive terms is Rs 50, we can conclude that the differences are equal.

### Conclusion:
- Since the difference between consecutive terms is constant, the series of costs forms an arithmetic progression (AP).

### Summary:
The costs of digging a well after every meter, starting from Rs 150 and increasing by Rs 50 for each subsequent meter, indeed make an arithmetic progression.

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