# Q : 1    In which of the following situations, does the list of numbers involved make an arithmetic progression, and why?           (iii) The cost of digging a well after every metre of digging, when it costs    for the first metre and rises by    for each subsequent metre.

It is given that
Cost of digging of 1st meter = Rs 150
and
rises by    for each subsequent metre
Therefore,

Cost of digging of first 2 meters = cost of digging of first meter + cost of digging additional meter

Cost of digging of first 2 meters = 150 + 50

=  Rs 200

SImilarly,
Cost of digging of first 3 meters = cost of digging of first 2 meters + cost of digging of additional meter

Cost of digging of first 3 meters = 200 + 50

=  Rs 250

We can clearly see that 150 ,200,250, ... is in AP with each subsequent term is obtained by adding a fixed number (50) to the previous term.

Therefore, it is an AP with first term (a) = 150 and common difference (d) = 50

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