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

Given:

The cost of digging a well after every metre of digging, when it costs Rs. 150 for the first metre and rises by Rs. 50 for each subsequent metre.

To do:

We have to check whether the sequence formed by the above information is an A.P.

Solution:

The cost of digging the well for the first metre$= Rs.\ 150$. 

The cost of digging the well for the second metre$= Rs.\ (150+50)=Rs.\ 200$.

The cost of digging the well for the third metre$= Rs.\ (200+50)=Rs.\ 250$.

The cost of digging the well for the fourth metre$= Rs.\ (250+50)=Rs.\ 300$.

The cost of digging the well for each successive metre (in rupees) forms the below sequence

$150, 200, 250, 300, ........$

Here, $a=150$ and $d=200-150=50$.

Therefore, the sequence of the numbers formed is an A.P. 

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Updated on: 10-Oct-2022

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