In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?

The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

Question

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Anonymous · Accepted Answer

Cost of digging the well after 1 metre of digging of Rs. 150 = a₄Cost of digging the well after 2 metres of digging
= Rs. 150 + Rs. 50
= Rs. 200 = a₂Cost of digging the well after 3 metres of digging
= Rs. 150 + Rs. 50
= Rs. 2a = a₃Cost of digging the well after 4 metres of digging
= Rs. 200 + Rs. 50
= Rs. 250 = a₄and so on.
a₂ – a₄ = Rs. 200 – Rs. 150 = Rs. 50
a₃ – a₂ = Rs. 250 – Rs. 200 = Rs. 50
a₄ – a₃ = Rs. 350 – Rs. 250 = Rs. 50
i.e., a_{k +1} – a_k is the same every time.
So this list of numbers forms an A .P. with the first term a Rs. 150 and the common difference d = Rs. 50.

Arithmetic Progressions

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.

In which of the following situational, does the list of numbers involved make an arithmetic progression, and why?
The cost of digging a well for the first metre is Rs. 150 and rises by Rs. 50 for each succeeding metre.